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Extremes and recurrence in dynamical systems /
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken, New Jersey :
John Wiley & Sons, Inc.,
[2016]
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Title Page; COPYRIGHT; Table of Contents; DEDICATION; CHAPTER 1: INTRODUCTION; 1.1 A TRANSDISCIPLINARY RESEARCH AREA; 1.2 SOME MATHEMATICAL IDEAS; 1.3 SOME DIFFICULTIES AND CHALLENGES IN STUDYING EXTREMES; 1.4 EXTREMES, OBSERVABLES, AND DYNAMICS; 1.5 THIS BOOK; ACKNOWLEDGMENTS; CHAPTER 2: A FRAMEWORK FOR RARE EVENTS IN STOCHASTIC PROCESSES AND DYNAMICAL SYSTEMS; 2.1 Introducing Rare Events; 2.2 Extremal Order Statistics; 2.3 Extremes and Dynamics; CHAPTER 3: CLASSICAL EXTREME VALUE THEORY; 3.1 THE i.i.d. SETTING AND THE CLASSICAL RESULTS; 3.2 STATIONARY SEQUENCES AND DEPENDENCE CONDITIONS.
- 5.1 INTRODUCTION TO HITTING AND RETURN TIME STATISTICS5.2 HTS VERSUS RTS AND POSSIBLE LIMIT LAWS; 5.3 THE LINK BETWEEN HITTING TIMES AND EXTREME VALUES; 5.4 UNIFORMLY HYPERBOLIC SYSTEMS; 5.5 NONUNIFORMLY HYPERBOLIC SYSTEMS; 5.6 NONEXPONENTIAL LAWS; CHAPTER 6: EXTREME VALUE THEORY FOR SELECTED DYNAMICAL SYSTEMS; 6.1 RARE EVENTS AND DYNAMICAL SYSTEMS; 6.2 INTRODUCTION AND BACKGROUND ON EXTREMES IN DYNAMICAL SYSTEMS; 6.3 THE BLOCKING ARGUMENT FOR NONUNIFORMLY EXPANDING SYSTEMS; 6.4 NONUNIFORMLY EXPANDING DYNAMICAL SYSTEMS; 6.5 NONUNIFORMLY HYPERBOLIC SYSTEMS; 6.6 HYPERBOLIC DYNAMICAL SYSTEMS.
- 6.7 SKEW-PRODUCT EXTENSIONS OF DYNAMICAL SYSTEMS6.8 ON THE RATE OF CONVERGENCE TO AN EXTREME VALUE DISTRIBUTION; 6.9 EXTREME VALUE THEORY FOR DETERMINISTIC FLOWS; 6.10 PHYSICAL OBSERVABLES AND EXTREME VALUE THEORY; 6.11 NONUNIFORMLY HYPERBOLIC EXAMPLES: THE HÉNON AND LOZI MAPS; 6.12 Extreme Value Statistics for the Lorenz '63 Model; CHAPTER 7: EXTREME VALUE THEORY FOR RANDOMLY PERTURBED DYNAMICAL SYSTEMS; 7.1 INTRODUCTION; 7.2 Random Transformations via the Probabilistic Approach: Additive Noise; 7.3 Random Transformations via the Spectral Approach.
- 7.4 RANDOM TRANSFORMATIONS VIA THE PROBABILISTIC APPROACH: RANDOMLY APPLIED STOCHASTIC PERTURBATIONS7.5 OBSERVATIONAL NOISE; 7.6 NONSTATIONARITY-THE SEQUENTIAL CASE; CHAPTER 8: A STATISTICAL MECHANICAL POINT OF VIEW; 8.1 CHOOSING A MATHEMATICAL FRAMEWORK; 8.2 GENERALIZED PARETO DISTRIBUTIONS FOR OBSERVABLES OF DYNAMICAL SYSTEMS; 8.3 IMPACTS OF PERTURBATIONS: RESPONSE THEORY FOR EXTREMES; 8.4 REMARKS ON THE GEOMETRY AND THE SYMMETRIES OF THE PROBLEM; CHAPTER 9: Extremes as Dynamical and Geometrical Indicators; 9.1 The Block Maxima Approach; 9.2 The Peaks Over Threshold Approach.