| Author |
Berger, Arno, 1968-
|
| Title |
Chaos and chance : an introduction to stochastic aspects of dynamics / Arno Berger. |
| OCLC |
47177018 |
| ISBN |
3110169908 (pbk. : alk. paper) |
|
3110169916 (hardcover) |
| Publisher |
Berlin ; New York : Walter de Gruyter, 2001. |
| Description |
x, 245 pages : illustrations ; 25 cm |
| LC Subject heading/s |
Differentiable dynamical systems.
|
|
Chaotic behavior in systems.
|
| Bibliography |
Includes bibliographical references and index. |
| Contents |
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. |
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