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Fractal geometry : mathematical foundations and applications / Kenneth Falconer
| Fractal geometry : mathematical foundations and applications / Kenneth Falconer |
| Autore | Falconer, Kenneth J. |
| Pubbl/distr/stampa | Chichester : J. Wiley & Sons, c1990 |
| Descrizione fisica | xxii, 288 p. : ill. ; 24 cm. |
| Disciplina | 514.742 |
| Soggetto topico | Fractals |
| ISBN | 0471922870 |
| Classificazione |
AMS 28A80
LC QA614.86.F35 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000910579707536 |
Falconer, Kenneth J.
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| Chichester : J. Wiley & Sons, c1990 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Fractal geometry and dynamical systems in pure and applied mathematics I : fractals in pure mathematics / / David Carfi [and three others], editors
| Fractal geometry and dynamical systems in pure and applied mathematics I : fractals in pure mathematics / / David Carfi [and three others], editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| Descrizione fisica | 1 online resource (410 p.) |
| Disciplina | 514/.742 |
| Collana | Contemporary Mathematics |
| Soggetto topico | Fractals |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-1082-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Preface""; ""Separation Conditions for Iterated Function Systems with Overlaps""; ""1. Introduction""; ""2. Preliminaries""; ""3. The finite type condition""; ""4. More on the finite type condition""; ""5. Generalized finite type condition""; ""6. Weak separation condition""; ""References""; "" -point Configurations of Discrete Self-Similar Sets""; ""1. Introduction""; ""2. Lower bounds for -point configurations of compatible fractals""; ""3. Determinant fractal zeta functions""; ""References""
""Fractal Complex Dimensions, Riemann Hypothesis and Invertibility of the Spectral Operator""""1. Introduction""; ""2. Generalized Fractal Strings and Their Complex Dimensions""; ""2.1. The geometry and spectra of ordinary fractal strings.""; ""2.2. Generalized fractal strings and their explicit formulas.""; ""3. The Spectral Operator _{ } and the Infinitesimal Shifts â??_{ }""; ""3.1. A â€?heuristicâ€? definition of _{ }.""; ""3.2. The weighted Hilbert space â??_{ }.""; ""3.3. The infinitesimal shifts â??_{ } and their properties.""; ""3.4. The spectral operator _{ }."" ""4. Inverse and Direct Spectral Problems for Fractal Strings""""4.1. The original inverse spectral problem.""; ""4.2. Fractal strings and the (modified) Weylâ€?Berry conjecture.""; ""5. Quasi-Invertibility and Almost Invertibility of the Spectral Operator""; ""5.1. The truncated operators â??^{( )}_{ } and ^{( )}_{ }.""; ""5.2. The spectra of â??_{ }^{( )} and ^{( )}_{ }.""; ""5.3. Quasi-invertibility of _{ }, almost invertibility and Riemann zeroes.""; ""6. Spectral Reformulations of the Riemann Hypothesis and of Almost RH"" ""6.1. Quasi-invertibility of _{ } and spectral reformulation of RH""""6.2. Almost invertibility of _{ } and spectral reformulation of “Almost RHâ€?.""; ""6.3. Invertibility of the spectral operator and phase transitions.""; ""7. Concluding Comments""; ""7.1. Extension to arithmetic zeta functions.""; ""7.2. Operator-valued Euler products.""; ""7.3. Global spectral operator.""; ""7.4. Towards a quantization of number theory.""; ""8. Appendix A:Riemannâ€?s Explicit Formula""; ""9. Appendix B:The Momentum Operator and Normality of â??_{ }""; ""References"" ""Analysis and Geometry of the Measurable Riemannian Structure on the SierpiÅ?ski Gasket""""1. Introduction""; ""2. SierpiÅ?ski gasket and its standard Dirichlet form""; ""3. Measurable Riemannian structure on the SierpiÅ?ski gasket""; ""4. Geometry under the measurable Riemannian structure""; ""5. Short time asymptotics of the heat kernels""; ""5.1. Intricsic metrics and off-diagonal Gaussian behavior""; ""5.2. One-dimensional asymptotics at vertices""; ""5.3. On-diagonal asymptotics at almost every point""; ""6. Ahlfors regularity and singularity of Hausdorff measure"" ""7. Weylâ€?s Laplacian eigenvalue asymptotics"" |
| Record Nr. | UNINA-9910480591203321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractal geometry and dynamical systems in pure and applied mathematics I : fractals in pure mathematics / / David Carfi [and three others], editors
| Fractal geometry and dynamical systems in pure and applied mathematics I : fractals in pure mathematics / / David Carfi [and three others], editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| Descrizione fisica | 1 online resource (410 p.) |
| Disciplina | 514/.742 |
| Collana | Contemporary mathematics |
| Soggetto topico | Fractals |
| ISBN | 1-4704-1082-6 |
| Classificazione | 28A1228A7828A8011M2611M4137A4537C4537F1058B2058C40 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Separation Conditions for Iterated Function Systems with Overlaps -- 1 Introduction -- 2 Preliminaries -- 3 The finite type condition -- 4 More on the finite type condition -- 5 Generalized finite type condition -- 6 Weak separation condition -- References -- -point Configurations of Discrete Self-Similar Sets -- 1 Introduction -- 2 Lower bounds for -point configurations of compatible fractals -- 3 Determinant fractal zeta functions -- References -- Fractal Complex Dimensions, Riemann Hypothesis and Invertibility of the Spectral Operator -- 1 Introduction -- 2 Generalized Fractal Strings and Their Complex Dimensions -- 3 The Spectral Operator and the Infinitesimal Shifts -- 4 Inverse and Direct Spectral Problems for Fractal Strings -- 5 Quasi-Invertibility and Almost Invertibility of the Spectral Operator -- 6 Spectral Reformulations of the Riemann Hypothesis and of Almost RH -- 7 Concluding Comments -- 8 Appendix A: Riemann's Explicit Formula -- 9 Appendix B: The Momentum Operator and Normality of -- References -- Analysis and Geometry of the Measurable Riemannian Structure on the SierpiÅski Gasket -- 1 Introduction -- 2 SierpiÅski gasket and its standard Dirichlet form -- 3 Measurable Riemannian structure on the SierpiÅski gasket -- 4 Geometry under the measurable Riemannian structure -- 5 Short time asymptotics of the heat kernels -- 6 Ahlfors regularity and singularity of Hausdorff measure -- 7 Weyl's Laplacian eigenvalue asymptotics cont. |
| Record Nr. | UNINA-9910796036303321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractal geometry and dynamical systems in pure and applied mathematics I : fractals in pure mathematics / / David Carfi [and three others], editors
| Fractal geometry and dynamical systems in pure and applied mathematics I : fractals in pure mathematics / / David Carfi [and three others], editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| Descrizione fisica | 1 online resource (410 p.) |
| Disciplina | 514/.742 |
| Collana | Contemporary mathematics |
| Soggetto topico | Fractals |
| ISBN | 1-4704-1082-6 |
| Classificazione | 28A1228A7828A8011M2611M4137A4537C4537F1058B2058C40 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Separation Conditions for Iterated Function Systems with Overlaps -- 1 Introduction -- 2 Preliminaries -- 3 The finite type condition -- 4 More on the finite type condition -- 5 Generalized finite type condition -- 6 Weak separation condition -- References -- -point Configurations of Discrete Self-Similar Sets -- 1 Introduction -- 2 Lower bounds for -point configurations of compatible fractals -- 3 Determinant fractal zeta functions -- References -- Fractal Complex Dimensions, Riemann Hypothesis and Invertibility of the Spectral Operator -- 1 Introduction -- 2 Generalized Fractal Strings and Their Complex Dimensions -- 3 The Spectral Operator and the Infinitesimal Shifts -- 4 Inverse and Direct Spectral Problems for Fractal Strings -- 5 Quasi-Invertibility and Almost Invertibility of the Spectral Operator -- 6 Spectral Reformulations of the Riemann Hypothesis and of Almost RH -- 7 Concluding Comments -- 8 Appendix A: Riemann's Explicit Formula -- 9 Appendix B: The Momentum Operator and Normality of -- References -- Analysis and Geometry of the Measurable Riemannian Structure on the SierpiÅski Gasket -- 1 Introduction -- 2 SierpiÅski gasket and its standard Dirichlet form -- 3 Measurable Riemannian structure on the SierpiÅski gasket -- 4 Geometry under the measurable Riemannian structure -- 5 Short time asymptotics of the heat kernels -- 6 Ahlfors regularity and singularity of Hausdorff measure -- 7 Weyl's Laplacian eigenvalue asymptotics cont. |
| Record Nr. | UNINA-9910827630003321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractal geometry and dynamical systems in pure and applied mathematics II : fractals in applied mathematics / / David Carfi [and three others], editors
| Fractal geometry and dynamical systems in pure and applied mathematics II : fractals in applied mathematics / / David Carfi [and three others], editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| Descrizione fisica | 1 online resource (384 p.) |
| Disciplina | 514/.742 |
| Collana | Contemporary Mathematics |
| Soggetto topico | Fractals |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-1083-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Preface""; ""Statistical Mechanics and Quantum Fields on Fractals""; ""1. Introduction""; ""2. Discrete scaling symmetry - Self similarity - Definitions""; ""3. Heat kernel and spectral functions - Generalities""; ""4. Laplacian on fractals - Heat kernel and spectral zeta function""; ""5. Thermodynamics on photons : The fractal blackbody [34]""; ""6. Conclusion and some open questions""; ""Acknowledgments""; ""References""; ""Spectral Algebra of the Chernov and Bogoslovsky Finsler Metric Tensors""; ""Preliminaries""; ""1. Spectral theory prerequisites""
""2. Spectral results for low dimensions""""3. Conclusions""; ""References""; ""Local Multifractal Analysis""; ""1. Introduction""; ""2. Properties of the local Hausdorff dimension and the local multifractal spectrum""; ""3. A local multifractal formalism for a dyadic family""; ""4. Measures with varying local spectrum""; ""5. Local spectrum of stochastic processes""; ""6. Other regularity exponents characterized by dyadic families""; ""7. A functional analysis point of view""; ""Acknowledgement""; ""References""; ""Extreme Risk and Fractal Regularity in Finance""; ""1. Introduction"" ""2. Fractal Regularities in Financial Markets""""3. The Markov-Switching Multifractal (MSM)""; ""4. Pricing Multifractal Risk""; ""5. Conclusion""; ""References""; ""An Algorithm for Dynamical Games with Fractal-Like Trajectories""; ""1. Introduction""; ""2. Preliminaries and notations""; ""3. The method for ¹ games""; ""4. Two players parametric games""; ""5. The algorithm""; ""6. Examples""; ""7. Final Remarks""; ""8. Resume""; ""9. Conclusions""; ""References""; ""The Landscape of Anderson Localization in a Disordered Medium""; ""1. Introduction""; ""2. Preliminaries"" ""Non-Regularly Varying and Non-Periodic Oscillation of the On-Diagonal Heat Kernels on Self-Similar Fractals""""1. Introduction""; ""2. Framework and main results""; ""3. Proof of Theorems 2.17 and 2.18""; ""4. Post-critically finite self-similar fractals""; ""4.1. Harmonic structures and resulting self-similar Dirichlet spaces""; ""4.2. Cases with good symmetry and affine nested fractals""; ""4.3. Cases possibly without good symmetry""; ""5. SierpiÅ?ski carpets""; ""References""; ""Lattice Effects in the Scaling Limit of the Two-Dimensional Self-Avoiding Walk""; ""1. Introduction"" ""2. Lattice effects"" |
| Record Nr. | UNINA-9910480582803321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractal geometry and dynamical systems in pure and applied mathematics II : fractals in applied mathematics / / David Carfi [and three others], editors
| Fractal geometry and dynamical systems in pure and applied mathematics II : fractals in applied mathematics / / David Carfi [and three others], editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| Descrizione fisica | 1 online resource (384 p.) |
| Disciplina | 514/.742 |
| Collana | Contemporary mathematics |
| Soggetto topico | Fractals |
| ISBN | 1-4704-1083-4 |
| Classificazione | 28A1228A7828A8011M2611M4137A4537C4537F1058B2058C40 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Statistical Mechanics and Quantum Fields on Fractals -- 1. Introduction -- 2. Discrete scaling symmetry - Self similarity - Definitions -- 3. Heat kernel and spectral functions - Generalities -- 4. Laplacian on fractals - Heat kernel and spectral zeta function -- 5. Thermodynamics on photons : The fractal blackbody [34] -- 6. Conclusion and some open questions -- Acknowledgments -- References -- Spectral Algebra of the Chernov and Bogoslovsky Finsler Metric Tensors -- Preliminaries -- 1. Spectral theory prerequisites -- 2. Spectral results for low dimensions -- 3. Conclusions -- References -- Local Multifractal Analysis -- 1. Introduction -- 2. Properties of the local Hausdorff dimension and the local multifractal spectrum -- 3. A local multifractal formalism for a dyadic family -- 4. Measures with varying local spectrum -- 5. Local spectrum of stochastic processes -- 6. Other regularity exponents characterized by dyadic families -- 7. A functional analysis point of view -- Acknowledgement -- References -- Extreme Risk and Fractal Regularity in Finance -- 1. Introduction -- 2. Fractal Regularities in Financial Markets -- 3. The Markov-Switching Multifractal (MSM) -- 4. Pricing Multifractal Risk -- 5. Conclusion -- References -- An Algorithm for Dynamical Games with Fractal-Like Trajectories -- 1. Introduction -- 2. Preliminaries and notations -- 3. The method for ¹ games -- 4. Two players parametric games -- 5. The algorithm -- 6. Examples -- 7. Final Remarks -- 8. Resume -- 9. Conclusions -- References -- The Landscape of Anderson Localization in a Disordered Medium -- 1. Introduction -- 2. Preliminaries -- Non-Regularly Varying and Non-Periodic Oscillation of the On-Diagonal Heat Kernels on Self-Similar Fractals -- 1. Introduction -- 2. Framework and main results -- 3. Proof of Theorems 2.17 and 2.18 -- 4. Post-critically finite self-similar fractals -- 4.1. Harmonic structures and resulting self-similar Dirichlet spaces -- 4.2. Cases with good symmetry and affine nested fractals -- 4.3. Cases possibly without good symmetry -- 5. SierpiÅ?ski carpets -- References -- Lattice Effects in the Scaling Limit of the Two-Dimensional Self-Avoiding Walk -- 1. Introduction -- 2. Lattice effects. |
| Record Nr. | UNINA-9910796036403321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractal geometry and dynamical systems in pure and applied mathematics II : fractals in applied mathematics / / David Carfi [and three others], editors
| Fractal geometry and dynamical systems in pure and applied mathematics II : fractals in applied mathematics / / David Carfi [and three others], editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| Descrizione fisica | 1 online resource (384 p.) |
| Disciplina | 514/.742 |
| Collana | Contemporary mathematics |
| Soggetto topico | Fractals |
| ISBN | 1-4704-1083-4 |
| Classificazione | 28A1228A7828A8011M2611M4137A4537C4537F1058B2058C40 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Statistical Mechanics and Quantum Fields on Fractals -- 1. Introduction -- 2. Discrete scaling symmetry - Self similarity - Definitions -- 3. Heat kernel and spectral functions - Generalities -- 4. Laplacian on fractals - Heat kernel and spectral zeta function -- 5. Thermodynamics on photons : The fractal blackbody [34] -- 6. Conclusion and some open questions -- Acknowledgments -- References -- Spectral Algebra of the Chernov and Bogoslovsky Finsler Metric Tensors -- Preliminaries -- 1. Spectral theory prerequisites -- 2. Spectral results for low dimensions -- 3. Conclusions -- References -- Local Multifractal Analysis -- 1. Introduction -- 2. Properties of the local Hausdorff dimension and the local multifractal spectrum -- 3. A local multifractal formalism for a dyadic family -- 4. Measures with varying local spectrum -- 5. Local spectrum of stochastic processes -- 6. Other regularity exponents characterized by dyadic families -- 7. A functional analysis point of view -- Acknowledgement -- References -- Extreme Risk and Fractal Regularity in Finance -- 1. Introduction -- 2. Fractal Regularities in Financial Markets -- 3. The Markov-Switching Multifractal (MSM) -- 4. Pricing Multifractal Risk -- 5. Conclusion -- References -- An Algorithm for Dynamical Games with Fractal-Like Trajectories -- 1. Introduction -- 2. Preliminaries and notations -- 3. The method for ¹ games -- 4. Two players parametric games -- 5. The algorithm -- 6. Examples -- 7. Final Remarks -- 8. Resume -- 9. Conclusions -- References -- The Landscape of Anderson Localization in a Disordered Medium -- 1. Introduction -- 2. Preliminaries -- Non-Regularly Varying and Non-Periodic Oscillation of the On-Diagonal Heat Kernels on Self-Similar Fractals -- 1. Introduction -- 2. Framework and main results -- 3. Proof of Theorems 2.17 and 2.18 -- 4. Post-critically finite self-similar fractals -- 4.1. Harmonic structures and resulting self-similar Dirichlet spaces -- 4.2. Cases with good symmetry and affine nested fractals -- 4.3. Cases possibly without good symmetry -- 5. SierpiÅ?ski carpets -- References -- Lattice Effects in the Scaling Limit of the Two-Dimensional Self-Avoiding Walk -- 1. Introduction -- 2. Lattice effects. |
| Record Nr. | UNINA-9910829158903321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractal geometry and stochastics VI / / Uta Freiberg, Ben Hambly, Michael Hinz and Steffen Winter (editors)
| Fractal geometry and stochastics VI / / Uta Freiberg, Ben Hambly, Michael Hinz and Steffen Winter (editors) |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (312 pages) : illustrations |
| Disciplina | 514.742 |
| Collana | Progress in Probability |
| Soggetto topico |
Fractals
Stochastic processes Processos estocàstics |
| Soggetto genere / forma |
Congressos
Llibres electrònics |
| ISBN | 3-030-59649-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996466552003316 |
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Fractal geometry and stochastics VI / / Uta Freiberg, Ben Hambly, Michael Hinz and Steffen Winter (editors)
| Fractal geometry and stochastics VI / / Uta Freiberg, Ben Hambly, Michael Hinz and Steffen Winter (editors) |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (312 pages) : illustrations |
| Disciplina | 514.742 |
| Collana | Progress in Probability |
| Soggetto topico |
Fractals
Stochastic processes Processos estocàstics |
| Soggetto genere / forma |
Congressos
Llibres electrònics |
| ISBN | 3-030-59649-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910485142703321 |
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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The fractal geometry of nature / Benoit B. Mandelbrot
| The fractal geometry of nature / Benoit B. Mandelbrot |
| Autore | Mandelbrot, Benoit B. |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | New York : W.H. Freeman and Company, 1982 |
| Descrizione fisica | 468 p. ; 23 cm. |
| Soggetto topico | Fractals |
| ISBN | 0716711869 |
| Classificazione |
53.1.65
53.9 516'.15 QA447.M357 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000961939707536 |
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Mandelbrot, Benoit B.
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| New York : W.H. Freeman and Company, 1982 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Soggetto topico
-
Fractals
(181)
- Chaotic behavior in systems (31)
- Dynamics (9)
- Wavelets (Mathematics) (9)
- Stochastic processes (7)