Chaos and chance : an introduction to stochastic aspects of dynamics / Arno Berger
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| Autore: |
Berger, Arno
|
| Titolo: |
Chaos and chance : an introduction to stochastic aspects of dynamics / Arno Berger
|
| Pubblicazione: | Berlin ; New York : Walter de Gruyter, 2001 |
| Descrizione fisica: | x, 245 p. : ill. ; 24 cm |
| Disciplina: | 515.352 |
| Soggetto topico: | Differentiable dynamical systems |
| Chaotic behavior in systems | |
| Classificazione: | AMS 37-01 |
| AMS 37A50 | |
| AMS 37A30 | |
| AMS 70K55 | |
| LC QA614.8.B48 | |
| 53.1.65 | |
| Nota di bibliografia: | Includes bibliographical references (p. [237]-240) and index |
| Nota di contenuto: | Introduction. Long-time behaviour of mechanical systems ; Iteration of maps ; Elementary stochastic processes ; Basic aspects of discrete dynamical systems. Hyperbolicity and bifurcations ; How may simple systems become complicated? Facing deterministic chaos ; Symbolic dynamical systems ; The emergence of chaos ; Newton's method for polynomials: a case study ; Circle maps, rotation numbers, and minimality ; Gimpses of billiards ; Horseshoes, attractors, and natural extensions ; Toral maps and shadowing ; Ergodic theory I. Foundations. The statistical point of view ; Invariant and ergodic measures ; Ergodic theorems ; Aspects of mixing ; Mixing properties ; The concept of entropy ; Ergodic theory II: Applications. The Frobenius-Perron operator ; Asymptotic behaviour of densities ; Piecewise expanding Markov maps ; A short look at Markov chains ; Class structure, absorption probabilities, and hitting times ; Recurrence and transience: dynamical classification of states ; The long-time behaviour of Markov chains ; The dynamical evolution of measures : Basic examples and concepts ; Asymptotic stability ; Back to geometry: fractal sets and measures ; Three final examples ; Searching for non-normal numbers ; The fractal nature of Brownian paths ; Patterns of congruence in the Pascal triangle |
| ISBN: | 3110169916 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 991000160479707536 |
| Lo trovi qui: | Univ. del Salento |
| Localizzazioni e accesso elettronico | http://www.loc.gov/catdir/toc/fy031/2001042161.html |
| Opac: | Controlla la disponibilità qui |
Serie:
De Gruyter textbook