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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 |
| 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 |
| 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 | ||
| ||