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

• Pubblicazione: Singapore : , : Springer, , [2021]; ©2021
• Descrizione fisica: 1 online resource (278 pages)
• Disciplina: 970
• Soggetto topico: Dynamics; Dinàmica topològica; Processament de dades
• Soggetto genere / forma: Congressos; Llibres electrònics
• Persona (resp. second.): DevaneyRobert L. <1948->; ChanKit C.; Vinod KumarP. B.
• Nota di bibliografia: Includes bibliographical references.
• 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.
• Titolo autorizzato: Topological dynamics and topological data analysis
• ISBN: 981-16-0174-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910502997203321
• Lo trovi qui: Univ. Federico II
• Serie: Springer Proceedings in Mathematics and Statistics