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Complex dynamics : twenty-five years after the appearance of the Mandelbrot set : proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Complex Dynamics : Twenty-five Years after the Appearance of the Mandelbrot Set, June 13-17, 2004, Snowbird, Utah / / Robert L. Devaney, Linda Keen, editors
| Complex dynamics : twenty-five years after the appearance of the Mandelbrot set : proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Complex Dynamics : Twenty-five Years after the Appearance of the Mandelbrot Set, June 13-17, 2004, Snowbird, Utah / / Robert L. Devaney, Linda Keen, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2006] |
| Descrizione fisica | 1 online resource (218 p.) |
| Disciplina | 514/.742 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Mandelbrot sets
Dynamics System theory Mappings (Mathematics) Domains of holomorphy Polynomials Numbers, Complex |
| Soggetto genere / forma | Electronic books. |
| ISBN | 0-8218-7986-3 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Polynomial vector fields, dessins d'enfants, and circle packings""""Siegel disks whose boundaries have only two complementary domains""; ""Non-uniform porosity for a subset of some Julia sets""; ""The existence of conformal measures for some transcendental meromorphic functions""; ""Open problems"" |
| Record Nr. | UNINA-9910480120103321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2006] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Complex dynamics : twenty-five years after the appearance of the Mandelbrot set : proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Complex Dynamics : Twenty-five Years after the Appearance of the Mandelbrot Set, June 13-17, 2004, Snowbird, Utah / / Robert L. Devaney, Linda Keen, editors
| Complex dynamics : twenty-five years after the appearance of the Mandelbrot set : proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Complex Dynamics : Twenty-five Years after the Appearance of the Mandelbrot Set, June 13-17, 2004, Snowbird, Utah / / Robert L. Devaney, Linda Keen, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2006] |
| Descrizione fisica | 1 online resource (218 p.) |
| Disciplina | 514/.742 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Mandelbrot sets
Dynamics System theory Mappings (Mathematics) Domains of holomorphy Polynomials Numbers, Complex |
| ISBN | 0-8218-7986-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Polynomial vector fields, dessins d'enfants, and circle packings""""Siegel disks whose boundaries have only two complementary domains""; ""Non-uniform porosity for a subset of some Julia sets""; ""The existence of conformal measures for some transcendental meromorphic functions""; ""Open problems"" |
| Record Nr. | UNINA-9910788662103321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2006] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Complex dynamics : twenty-five years after the appearance of the Mandelbrot set : proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Complex Dynamics : Twenty-five Years after the Appearance of the Mandelbrot Set, June 13-17, 2004, Snowbird, Utah / / Robert L. Devaney, Linda Keen, editors
| Complex dynamics : twenty-five years after the appearance of the Mandelbrot set : proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Complex Dynamics : Twenty-five Years after the Appearance of the Mandelbrot Set, June 13-17, 2004, Snowbird, Utah / / Robert L. Devaney, Linda Keen, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2006] |
| Descrizione fisica | 1 online resource (218 p.) |
| Disciplina | 514/.742 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Mandelbrot sets
Dynamics System theory Mappings (Mathematics) Domains of holomorphy Polynomials Numbers, Complex |
| ISBN | 0-8218-7986-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Polynomial vector fields, dessins d'enfants, and circle packings""""Siegel disks whose boundaries have only two complementary domains""; ""Non-uniform porosity for a subset of some Julia sets""; ""The existence of conformal measures for some transcendental meromorphic functions""; ""Open problems"" |
| Record Nr. | UNINA-9910815366003321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2006] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential equations, dynamical systems, and an introduction to chaos / / Morris W. Hirsch, Stephen Smale, Robert L. Devaney [[electronic resource]]
| Differential equations, dynamical systems, and an introduction to chaos / / Morris W. Hirsch, Stephen Smale, Robert L. Devaney [[electronic resource]] |
| Autore | Hirsch Morris W. <1933-> |
| Edizione | [3rd ed.] |
| Pubbl/distr/stampa | Waltham, MA, : Academic Press, c2013 |
| Descrizione fisica | 1 online resource (xiv, 418 p. ) : ill. ; |
| Disciplina | 515/.35 |
| Altri autori (Persone) |
SmaleStephen <1930->
DevaneyRobert L. <1948-> |
| Soggetto topico |
Differential equations
Algebras, Linear Chaotic behavior in systems |
| Soggetto genere / forma | Electronic books |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910461730403321 |
Hirsch Morris W. <1933->
|
||
| Waltham, MA, : Academic Press, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential equations, dynamical systems, and an introduction to chaos / / Morris W. Hirsch, Stephen Smale, Robert L. Devaney [[electronic resource]]
| Differential equations, dynamical systems, and an introduction to chaos / / Morris W. Hirsch, Stephen Smale, Robert L. Devaney [[electronic resource]] |
| Autore | Hirsch Morris W. <1933-> |
| Edizione | [3rd ed.] |
| Pubbl/distr/stampa | Waltham, MA, : Academic Press, c2013 |
| Descrizione fisica | 1 online resource (xiv, 418 p. ) : ill. ; |
| Disciplina | 515/.35 |
| Altri autori (Persone) |
SmaleStephen <1930->
DevaneyRobert L. <1948-> |
| Soggetto topico |
Differential equations
Algebras, Linear Chaotic behavior in systems |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910790003803321 |
|
Hirsch Morris W. <1933->
|
||
| Waltham, MA, : Academic Press, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential equations, dynamical systems, and an introduction to chaos / / Morris W. Hirsch, Stephen Smale, Robert L. Devaney
| Differential equations, dynamical systems, and an introduction to chaos / / Morris W. Hirsch, Stephen Smale, Robert L. Devaney |
| Autore | Hirsch Morris W. <1933-> |
| Edizione | [3rd ed.] |
| Pubbl/distr/stampa | Waltham, MA, : Academic Press, c2013 |
| Descrizione fisica | 1 online resource (xiv, 418 p. ) : ill. ; |
| Disciplina | 515/.35 |
| Altri autori (Persone) |
SmaleStephen <1930->
DevaneyRobert L. <1948-> |
| Soggetto topico |
Differential equations
Algebras, Linear Chaotic behavior in systems |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Differential Equations, Dynamical Systems, and an Introduction to Chaos -- Copyright -- Table of Contents -- Preface to Third Edition -- Preface -- 1 First-Order Equations -- 1.1 The Simplest Example -- 1.2 The Logistic Population Model -- 1.3 Constant Harvesting and Bifurcations -- 1.4 Periodic Harvesting and Periodic Solutions -- 1.5 Computing the Poincaré Map -- 1.6 Exploration: A Two-Parameter Family -- Exercises -- 2 Planar Linear Systems -- 2.1 Second-Order Differential Equations -- 2.2 Planar Systems -- 2.3 Preliminaries from Algebra -- 2.4 Planar Linear Systems -- 2.5 Eigenvalues and Eigenvectors -- 2.6 Solving Linear Systems -- 2.7 The Linearity Principle -- Exercises -- 3 Phase Portraits for Planar Systems -- 3.1 Real Distinct Eigenvalues -- 3.2 Complex Eigenvalues -- 3.3 Repeated Eigenvalues -- 3.4 Changing Coordinates -- Exercises -- 4 Classification of Planar Systems -- 4.1 The Trace-Determinant Plane -- 4.2 Dynamical Classification -- Case 1 -- Case 2 -- Case 3 -- 4.3 Exploration: A 3D Parameter Space -- Exercises -- 5 Higher-Dimensional Linear Algebra -- 5.1 Preliminaries from Linear Algebra -- 5.2 Eigenvalues and Eigenvectors -- 5.3 Complex Eigenvalues -- 5.4 Bases and Subspaces -- 5.5 Repeated Eigenvalues -- 5.6 Genericity -- Exercises -- 6 Higher-Dimensional Linear Systems -- 6.1 Distinct Eigenvalues -- 6.2 Harmonic Oscillators -- 6.3 Repeated Eigenvalues -- 6.4 The Exponential of a Matrix -- 6.5 Nonautonomous Linear Systems -- Exercises -- 7 Nonlinear Systems -- 7.1 Dynamical Systems -- 7.2 The Existence and Uniqueness Theorem -- 7.3 Continuous Dependence of Solutions -- 7.4 The Variational Equation -- 7.5 Exploration: Numerical Methods -- 7.6 Exploration: Numerical Methods and Chaos -- Exercises -- 8 Equilibria in Nonlinear Systems -- 8.1 Some Illustrative Examples -- 8.2 Nonlinear Sinks and Sources -- 8.3 Saddles.
8.4 Stability -- 8.5 Bifurcations -- 8.6 Exploration: Complex Vector Fields -- Exercises -- 9 Global Nonlinear Techniques -- 9.1 Nullclines -- 9.2 Stability of Equilibria -- 9.3 Gradient Systems -- 9.4 Hamiltonian Systems -- 9.5 Exploration: The Pendulum with Constant Forcing -- Exercises -- 10 Closed Orbits and Limit Sets -- 10.1 Limit Sets -- 10.2 Local Sections and Flow Boxes -- 10.3 The Poincaré Map -- 10.4 Monotone Sequences in Planar Dynamical Systems -- 10.5 The Poincaré-Bendixson Theorem -- 10.6 Applications of Poincaré-Bendixson -- 10.7 Exploration: Chemical Reactions that Oscillate -- Exercises -- 11 Applications in Biology -- 11.1 Infectious Diseases -- 11.2 Predator-Prey Systems -- 11.3 Competitive Species -- 11.4 Exploration: Competition and Harvesting -- 11.5 Exploration: Adding Zombies to the SIR Model -- Exercises -- 12 Applications in Circuit Theory -- 12.1 An RLC Circuit -- 12.2 The Liénard Equation -- 12.3 The van der Pol Equation -- 12.4 A Hopf Bifurcation -- 12.5 Exploration: Neurodynamics -- Exercises -- 13 Applications in Mechanics -- 13.1 Newton's Second Law -- 13.2 Conservative Systems -- 13.3 Central Force Fields -- 13.4 The Newtonian Central Force System -- 13.5 Kepler's First Law -- 13.6 The Two-Body Problem -- 13.7 Blowing up the Singularity -- 13.8 Exploration: Other Central Force Problems -- 13.9 Exploration: Classical Limits of Quantum Mechanical Systems -- 13.10 Exploration: Motion of a Glider -- Exercises -- 14 The Lorenz System -- 14.1 Introduction -- 14.2 Elementary Properties of the Lorenz System -- 14.3 The Lorenz Attractor -- 14.4 A Model for the Lorenz Attractor -- 14.5 The Chaotic Attractor -- 14.6 Exploration: The Rössler Attractor -- Exercises -- 15 Discrete Dynamical Systems -- 15.1 Introduction -- 15.2 Bifurcations -- 15.3 The Discrete Logistic Model -- 15.4 Chaos -- 15.5 Symbolic Dynamics. 15.6 The Shift Map -- 15.7 The Cantor Middle-Thirds Set -- 15.8 Exploration: Cubic Chaos -- 15.9 Exploration: The Orbit Diagram -- Exercises -- 16 Homoclinic Phenomena -- 16.1 The Shilnikov System -- 16.2 The Horseshoe Map -- 16.3 The Double Scroll Attractor -- 16.4 Homoclinic Bifurcations -- 16.5 Exploration: The Chua Circuit -- Exercises -- 17 Existence and Uniqueness Revisited -- 17.1 The Existence and Uniqueness Theorem -- 17.2 Proof of Existence and Uniqueness -- 17.3 Continuous Dependence on Initial Conditions -- 17.4 Extending Solutions -- 17.5 Nonautonomous Systems -- 17.6 Differentiability of the Flow -- Exercises -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- O -- P -- R -- S -- T -- U -- V -- W -- Z. |
| Record Nr. | UNINA-9910822005403321 |
|
Hirsch Morris W. <1933->
|
||
| Waltham, MA, : Academic Press, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Topological dynamics and topological data analysis : IWCTA 2018, Kochi, India, December 9-11 / / edited by Robert L. Devaney, Kit C. Chan, P. B. Vinod Kumar
| Topological dynamics and topological data analysis : IWCTA 2018, Kochi, India, December 9-11 / / edited by Robert L. Devaney, Kit C. Chan, P. B. Vinod Kumar |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (278 pages) |
| Disciplina | 970 |
| Collana | Springer Proceedings in Mathematics and Statistics |
| Soggetto topico |
Dynamics
Dinàmica topològica Processament de dades |
| Soggetto genere / forma |
Congressos
Llibres electrònics |
| ISBN | 981-16-0174-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- An Overview of Unimodal Inverse Limit Spaces -- 1 Introduction -- 2 Definitions and Notation -- 2.1 Chainability -- 2.2 Symbolic Dynamics -- 3 End points and Folding Points -- 4 Composants -- 5 Ingram Conjecture -- References -- Dimension Theory of Some Non-Markovian Repellers Part I: A Gentle Introduction -- 1 Introduction -- 2 Barnsley's Skew Product Maps -- 3 The Hausdorff and Box Dimensions -- 3.1 Fractal Dimensions of Sets -- 3.2 Hausdorff Dimension of Measures -- 4 Self-similar Sets -- 4.1 Self-similar Measures -- 5 Dimension of the Self-conformal Sets and Measures When OSC Holds -- 5.1 Hausdorff Dimension of Self-conformal Sets When OSC Is Assumed -- 5.2 Hausdorff Dimension of an Invariant Measure and Lyapunov Exponents -- 6 The Hausdorff Dimension of Self-affine Sets -- 6.1 Singular Value Function, Affinity Dimension, Falconer's Theorem -- 7 Ergodic Measures for a Self-affine IFS -- 7.1 Self-affine Measures -- 8 Ergodic Measures for Barnsley's Skew Product Maps -- 9 Hofbauer's Pressure -- 9.1 Pressure and Markov Sets -- 9.2 Conformal Measure and Small Cylinders -- 10 The Dimension of Barnsley's Repellers -- 10.1 The Basic Definitions -- 10.2 Diagonal and Essentially Non-diagonal System -- 10.3 Markov Pressure and Hofbauer Pressure -- 10.4 The Main Results -- References -- Dimension Theory of Some Non-Markovian Repellers Part II: Dynamically Defined Function Graphs -- 1 The Weierstrass and Takagi Functions -- 2 Dynamically Defined Function Graphs -- 3 Markovian Fractal Interpolation Functions -- 4 Continuous Generalized Takagi Functions -- References -- Iterated Function Systems-A Topological Approach. Attractors -- 1 Introduction -- 2 IFS -- 3 Basins and Pointwise Basins -- 4 Point-Fibred and Strongly Fibred Attractors -- 5 Fast Basins -- 6 Homoclinic Attractors Versus Fast Basins -- References.
Zero-Dimensional Covers of Dynamical Systems -- 1 Introduction -- 2 Preliminaries -- 3 Finite-to-one Zero-Dimensional Covers -- 4 Zero-Dimensional Decompositions of Dynamical Systems -- References -- Chaotic Continua in Chaotic Dynamical Systems -- 1 Introduction -- 2 Preliminaries -- 3 Free Tracing Property by Free G-chains -- 4 Positive Topological Entropy -- 5 Characterizations of Indecomposable Continua and Free Tracing Property -- References -- Mandelpinski Necklaces in the Parameter Planes of Rational Maps -- 1 Introduction -- 2 Elementary Mapping Properties -- 3 Some Special Cases -- 4 Rings in Dynamical Plane -- 5 Rings in Parameter Plane -- 6 The Special Case n = 2 -- References -- Some Examples of Hypercyclic Operators and Universal Sequences of Operators -- 1 Introduction -- 2 Entire Functions -- 3 Hilbert Spaces of Analytic Functions -- References -- Some Basic Properties of Hypercyclic Operators -- 1 Introduction -- 2 Common Hypercyclic Vectors -- 3 Hypercyclic Extension -- References -- The Testing Ground of Weighted Shift Operators for Hypercyclicity -- 1 Introduction -- 2 Weak Topologies -- 3 Orbital Limit Points -- 4 Hypercyclic Factorization -- References -- On δ-deformations of Polygonal Dendrites -- 1 Preliminaries -- 1.1 Self-similar Sets -- 1.2 Dendrites -- 1.3 Contractible Polygonal Systems -- 1.4 Main Parameters of a Contractible Polygonal System -- 2 Generalized Polygonal Systems -- 3 δ-deformations of Contractible Polygonal Systems -- 4 Parameter Matching Theorem -- 5 Main Theorem -- 5.1 Some Assumptions -- References -- General Position Theorem and Its Applications -- 1 Introduction -- 2 Definitions and Notations -- 3 General Position Theorem -- 4 Application of General Position Theorem to Self-similar Sets -- 4.1 Moving Subpieces Apart from Each Other. -- 4.2 Non-empty Overlaps of Prescribed Type -- References. The nth Itarate of a Map with Dense Orbit -- 1 Introduction -- 1.1 The General Separation Theorem -- References -- Periodic Points of N-Dimensional Toral Automorphisms -- 1 Introduction -- 2 Basic Results -- 3 Main Results -- 4 Summary -- References -- Julia Sets in Topological Spaces -- 1 Introduction -- 2 Basin of Attractors to a Point -- 3 Fatou and Julia Sets in General Topological Space -- 4 Locally Compact and T2 Space -- 5 Julia Sets -- 6 Conclusion -- References -- Julia Set of Some Graphs Using Independence Polynomials -- 1 Introduction -- 2 Preliminaries -- 3 Computing the Independence Polynomial -- 4 Complete Graph -- 4.1 Relation of Hausdorff Dimension and Energy of J(I(G,z)) of Complete Graph -- 4.2 Results on Complete Graph -- 5 Mandelbrot Graph -- 5.1 Classification of Mandelbrot Graphs -- 5.2 Julia Set of Reduced Independence Polynomial of Some Graphs -- 6 Independence Polynomial of Second Degree of Graphs -- 7 Conclusion -- References -- An Introduction to the Notion of Natural Pseudo-distance in Topological Data Analysis -- 1 Introduction -- 1.1 Related Literature and Historical Notes -- 2 The Definition of dG -- 2.1 The Role of dG in Topological Data Analysis -- 3 Theoretical Results About dG -- 3.1 Optimal Homeomorphisms -- 4 A Link Between dG and Persistent Homology -- 4.1 Persistent Homology -- 4.2 Group Equivariant Non-expansive Operators -- 4.3 Persistent Homology as a Tool to Get Lower Bounds for dG -- 5 An Open Problem -- References -- A Brief Introduction to Multidimensional Persistent Betti Numbers -- 1 Introduction -- 2 PBNs: Definitions and First Properties -- 2.1 1-Dimensional PBNs -- 2.2 The Foliation Method -- 3 Evaluating the Distance Between Multidimensional PBNs -- 3.1 Underlying Theoretical Results -- 4 An Algorithm for Approximating Dmatch -- 4.1 The 2-Dimensional Case. 5 Beyond the Multidimensional Matching Distance Dmatch -- 5.1 The Coherent Matching Distance for 2-Dimensional Persistent Betti Numbers -- References -- Some New Methods to Build Group Equivariant Non-expansive Operators in TDA -- 1 Introduction -- 2 Our Mathematical Model -- 3 Building New GENEOs by Means of Power Means -- 3.1 Examples -- 4 Series of GENEOs -- 5 Conclusions -- References -- Topological Stability of the Hippocampal Spatial Map and Synaptic Transience -- 1 Introduction -- 2 Overview of the Results -- 2.1 Decaying Clique Complexes -- 2.2 Finite Latency Complexes -- 3 Discussion -- References -- Intuitionistic Fuzzy Graph Morphological Topology -- 1 Introduction -- 2 Preliminaries -- 3 Morphological Topology -- 4 Conclusion -- References -- Some Properties of the Bitopological Space Associated With the 3-Uniform Semigraph of Cycle Graph -- 1 Introduction -- 2 3-Uniform Semigraph of a Cycle Graph -- 3 Bitopological Space -- 4 Bitopological Space on Cm,1 -- 5 Some Topological Properties of (V,τE',τM') -- 6 Conclusion -- References -- Hypergraph Topology -- 1 Introduction -- 2 Preliminaries -- 3 Hypergraph Topological Space -- 4 Closed Set -- 5 Continuity in Hypergraph Topology -- 6 Metric in Hypergraph Topology -- 7 Homeomorphism in Hypergraphs -- 7.1 Subdivision -- 7.2 Smoothing Out -- 8 Conclusion -- References. |
| Record Nr. | UNISA-996466387903316 |
| Singapore : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Topological dynamics and topological data analysis : IWCTA 2018, Kochi, India, December 9-11 / / edited by Robert L. Devaney, Kit C. Chan, P. B. Vinod Kumar
| Topological dynamics and topological data analysis : IWCTA 2018, Kochi, India, December 9-11 / / edited by Robert L. Devaney, Kit C. Chan, P. B. Vinod Kumar |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (278 pages) |
| Disciplina | 970 |
| Collana | Springer Proceedings in Mathematics and Statistics |
| Soggetto topico |
Dynamics
Dinàmica topològica Processament de dades |
| Soggetto genere / forma |
Congressos
Llibres electrònics |
| ISBN | 981-16-0174-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- An Overview of Unimodal Inverse Limit Spaces -- 1 Introduction -- 2 Definitions and Notation -- 2.1 Chainability -- 2.2 Symbolic Dynamics -- 3 End points and Folding Points -- 4 Composants -- 5 Ingram Conjecture -- References -- Dimension Theory of Some Non-Markovian Repellers Part I: A Gentle Introduction -- 1 Introduction -- 2 Barnsley's Skew Product Maps -- 3 The Hausdorff and Box Dimensions -- 3.1 Fractal Dimensions of Sets -- 3.2 Hausdorff Dimension of Measures -- 4 Self-similar Sets -- 4.1 Self-similar Measures -- 5 Dimension of the Self-conformal Sets and Measures When OSC Holds -- 5.1 Hausdorff Dimension of Self-conformal Sets When OSC Is Assumed -- 5.2 Hausdorff Dimension of an Invariant Measure and Lyapunov Exponents -- 6 The Hausdorff Dimension of Self-affine Sets -- 6.1 Singular Value Function, Affinity Dimension, Falconer's Theorem -- 7 Ergodic Measures for a Self-affine IFS -- 7.1 Self-affine Measures -- 8 Ergodic Measures for Barnsley's Skew Product Maps -- 9 Hofbauer's Pressure -- 9.1 Pressure and Markov Sets -- 9.2 Conformal Measure and Small Cylinders -- 10 The Dimension of Barnsley's Repellers -- 10.1 The Basic Definitions -- 10.2 Diagonal and Essentially Non-diagonal System -- 10.3 Markov Pressure and Hofbauer Pressure -- 10.4 The Main Results -- References -- Dimension Theory of Some Non-Markovian Repellers Part II: Dynamically Defined Function Graphs -- 1 The Weierstrass and Takagi Functions -- 2 Dynamically Defined Function Graphs -- 3 Markovian Fractal Interpolation Functions -- 4 Continuous Generalized Takagi Functions -- References -- Iterated Function Systems-A Topological Approach. Attractors -- 1 Introduction -- 2 IFS -- 3 Basins and Pointwise Basins -- 4 Point-Fibred and Strongly Fibred Attractors -- 5 Fast Basins -- 6 Homoclinic Attractors Versus Fast Basins -- References.
Zero-Dimensional Covers of Dynamical Systems -- 1 Introduction -- 2 Preliminaries -- 3 Finite-to-one Zero-Dimensional Covers -- 4 Zero-Dimensional Decompositions of Dynamical Systems -- References -- Chaotic Continua in Chaotic Dynamical Systems -- 1 Introduction -- 2 Preliminaries -- 3 Free Tracing Property by Free G-chains -- 4 Positive Topological Entropy -- 5 Characterizations of Indecomposable Continua and Free Tracing Property -- References -- Mandelpinski Necklaces in the Parameter Planes of Rational Maps -- 1 Introduction -- 2 Elementary Mapping Properties -- 3 Some Special Cases -- 4 Rings in Dynamical Plane -- 5 Rings in Parameter Plane -- 6 The Special Case n = 2 -- References -- Some Examples of Hypercyclic Operators and Universal Sequences of Operators -- 1 Introduction -- 2 Entire Functions -- 3 Hilbert Spaces of Analytic Functions -- References -- Some Basic Properties of Hypercyclic Operators -- 1 Introduction -- 2 Common Hypercyclic Vectors -- 3 Hypercyclic Extension -- References -- The Testing Ground of Weighted Shift Operators for Hypercyclicity -- 1 Introduction -- 2 Weak Topologies -- 3 Orbital Limit Points -- 4 Hypercyclic Factorization -- References -- On δ-deformations of Polygonal Dendrites -- 1 Preliminaries -- 1.1 Self-similar Sets -- 1.2 Dendrites -- 1.3 Contractible Polygonal Systems -- 1.4 Main Parameters of a Contractible Polygonal System -- 2 Generalized Polygonal Systems -- 3 δ-deformations of Contractible Polygonal Systems -- 4 Parameter Matching Theorem -- 5 Main Theorem -- 5.1 Some Assumptions -- References -- General Position Theorem and Its Applications -- 1 Introduction -- 2 Definitions and Notations -- 3 General Position Theorem -- 4 Application of General Position Theorem to Self-similar Sets -- 4.1 Moving Subpieces Apart from Each Other. -- 4.2 Non-empty Overlaps of Prescribed Type -- References. The nth Itarate of a Map with Dense Orbit -- 1 Introduction -- 1.1 The General Separation Theorem -- References -- Periodic Points of N-Dimensional Toral Automorphisms -- 1 Introduction -- 2 Basic Results -- 3 Main Results -- 4 Summary -- References -- Julia Sets in Topological Spaces -- 1 Introduction -- 2 Basin of Attractors to a Point -- 3 Fatou and Julia Sets in General Topological Space -- 4 Locally Compact and T2 Space -- 5 Julia Sets -- 6 Conclusion -- References -- Julia Set of Some Graphs Using Independence Polynomials -- 1 Introduction -- 2 Preliminaries -- 3 Computing the Independence Polynomial -- 4 Complete Graph -- 4.1 Relation of Hausdorff Dimension and Energy of J(I(G,z)) of Complete Graph -- 4.2 Results on Complete Graph -- 5 Mandelbrot Graph -- 5.1 Classification of Mandelbrot Graphs -- 5.2 Julia Set of Reduced Independence Polynomial of Some Graphs -- 6 Independence Polynomial of Second Degree of Graphs -- 7 Conclusion -- References -- An Introduction to the Notion of Natural Pseudo-distance in Topological Data Analysis -- 1 Introduction -- 1.1 Related Literature and Historical Notes -- 2 The Definition of dG -- 2.1 The Role of dG in Topological Data Analysis -- 3 Theoretical Results About dG -- 3.1 Optimal Homeomorphisms -- 4 A Link Between dG and Persistent Homology -- 4.1 Persistent Homology -- 4.2 Group Equivariant Non-expansive Operators -- 4.3 Persistent Homology as a Tool to Get Lower Bounds for dG -- 5 An Open Problem -- References -- A Brief Introduction to Multidimensional Persistent Betti Numbers -- 1 Introduction -- 2 PBNs: Definitions and First Properties -- 2.1 1-Dimensional PBNs -- 2.2 The Foliation Method -- 3 Evaluating the Distance Between Multidimensional PBNs -- 3.1 Underlying Theoretical Results -- 4 An Algorithm for Approximating Dmatch -- 4.1 The 2-Dimensional Case. 5 Beyond the Multidimensional Matching Distance Dmatch -- 5.1 The Coherent Matching Distance for 2-Dimensional Persistent Betti Numbers -- References -- Some New Methods to Build Group Equivariant Non-expansive Operators in TDA -- 1 Introduction -- 2 Our Mathematical Model -- 3 Building New GENEOs by Means of Power Means -- 3.1 Examples -- 4 Series of GENEOs -- 5 Conclusions -- References -- Topological Stability of the Hippocampal Spatial Map and Synaptic Transience -- 1 Introduction -- 2 Overview of the Results -- 2.1 Decaying Clique Complexes -- 2.2 Finite Latency Complexes -- 3 Discussion -- References -- Intuitionistic Fuzzy Graph Morphological Topology -- 1 Introduction -- 2 Preliminaries -- 3 Morphological Topology -- 4 Conclusion -- References -- Some Properties of the Bitopological Space Associated With the 3-Uniform Semigraph of Cycle Graph -- 1 Introduction -- 2 3-Uniform Semigraph of a Cycle Graph -- 3 Bitopological Space -- 4 Bitopological Space on Cm,1 -- 5 Some Topological Properties of (V,τE',τM') -- 6 Conclusion -- References -- Hypergraph Topology -- 1 Introduction -- 2 Preliminaries -- 3 Hypergraph Topological Space -- 4 Closed Set -- 5 Continuity in Hypergraph Topology -- 6 Metric in Hypergraph Topology -- 7 Homeomorphism in Hypergraphs -- 7.1 Subdivision -- 7.2 Smoothing Out -- 8 Conclusion -- References. |
| Record Nr. | UNINA-9910502997203321 |
| Singapore : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||