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- 2001042161 contributor B8946485.
- 2001042161 created "2001.".
- 2001042161 date "2001".
- 2001042161 date "2001.".
- 2001042161 dateCopyrighted "2001.".
- 2001042161 description "Includes bibliographical references and index.".
- 2001042161 description "Machine generated contents note: 1 Introduction -- 1.1 Long-time behaviour of mechanical systems-- 1.2 Iteration of maps-- 1.3 Elementary stochastic processes-- Exercises --2 Basic aspects of discrete dynamical systems -- 2.1 Hyperbolicity and bifurcations-- 2.2 How may simple systems become complicated ?-- 2.3 Facing deterministic chaos-- 2.3.1 Symbolic dynamical systems-- 2.3.2 The emergence of chaos-- 2.3.3 Newton's method for polynomials: a case study-- 2.4 Circle maps, rotation numbers, and minimality-- 2.5 Glimpses of billiards-- 2.6 Horseshoes, attractors, and natural extensions-- 2.7 Toral maps and shadowing-- Exercises-- -- 3 Ergodic theory I. Foundations -- 3.1 The statistical point of view-- 3.2 Invariant and ergodic measures-- 3.3 Ergodic theorems-- 3.4 Aspects of mixing-- 3.4.1 Mixing properties-- 3.4.2 The concept of entropy-- Exercises-- -- 4 Ergodic theory II. Applications -- 4.1 The Frobenius-Perron operator-- 4.2 Asymptotic behaviour of densities-- 4.3 Piecewise expanding Markov maps-- 4.4 A short look at Markov chains-- 4.4.1 Class structure, absorption probabilities, and hitting times. -- 4.4.2 Recurrence and transience: dynamical classification of states -- 4.4.3 The long-time behaviour of Markov chains-- Exercises-- -- 5 The dynamical evolution of measures -- 5.1 Basic examples and concepts-- 5.2 Asymptotic stability-- 5.3 Back to geometry: fractal sets and measures-- 5.4 Three final examples-- 5.4.1 Searching for non-normal numbers-- 5.4.2 The fractal nature of Brownian paths-- 5.4.3 Patterns of congruence in the Pascal triangle-- Exercises-- -- A The toolbox -- A.1 A survey of notations-- A.2 Basic facts from measure theory-- A.3 Integration theory-- A.4 Conditional expectations-- -- B A student's guide to the literature.".
- 2001042161 extent "x, 245 p. :".
- 2001042161 identifier "3110169908 (pbk. : alk. paper)".
- 2001042161 identifier 2001042161.html.
- 2001042161 issued "2001".
- 2001042161 issued "2001.".
- 2001042161 language "eng".
- 2001042161 publisher "Berlin ; New York : Walter de Gruyter,".
- 2001042161 subject "515/.352 21".
- 2001042161 subject "Chaotic behavior in systems.".
- 2001042161 subject "Differentiable dynamical systems.".
- 2001042161 subject "QA614.8 .B48 2001".
- 2001042161 tableOfContents "Machine generated contents note: 1 Introduction -- 1.1 Long-time behaviour of mechanical systems-- 1.2 Iteration of maps-- 1.3 Elementary stochastic processes-- Exercises --2 Basic aspects of discrete dynamical systems -- 2.1 Hyperbolicity and bifurcations-- 2.2 How may simple systems become complicated ?-- 2.3 Facing deterministic chaos-- 2.3.1 Symbolic dynamical systems-- 2.3.2 The emergence of chaos-- 2.3.3 Newton's method for polynomials: a case study-- 2.4 Circle maps, rotation numbers, and minimality-- 2.5 Glimpses of billiards-- 2.6 Horseshoes, attractors, and natural extensions-- 2.7 Toral maps and shadowing-- Exercises-- -- 3 Ergodic theory I. Foundations -- 3.1 The statistical point of view-- 3.2 Invariant and ergodic measures-- 3.3 Ergodic theorems-- 3.4 Aspects of mixing-- 3.4.1 Mixing properties-- 3.4.2 The concept of entropy-- Exercises-- -- 4 Ergodic theory II. Applications -- 4.1 The Frobenius-Perron operator-- 4.2 Asymptotic behaviour of densities-- 4.3 Piecewise expanding Markov maps-- 4.4 A short look at Markov chains-- 4.4.1 Class structure, absorption probabilities, and hitting times. -- 4.4.2 Recurrence and transience: dynamical classification of states -- 4.4.3 The long-time behaviour of Markov chains-- Exercises-- -- 5 The dynamical evolution of measures -- 5.1 Basic examples and concepts-- 5.2 Asymptotic stability-- 5.3 Back to geometry: fractal sets and measures-- 5.4 Three final examples-- 5.4.1 Searching for non-normal numbers-- 5.4.2 The fractal nature of Brownian paths-- 5.4.3 Patterns of congruence in the Pascal triangle-- Exercises-- -- A The toolbox -- A.1 A survey of notations-- A.2 Basic facts from measure theory-- A.3 Integration theory-- A.4 Conditional expectations-- -- B A student's guide to the literature.".
- 2001042161 title "Chaos and chance : an introduction to stochastic aspects of dynamics / Arno Berger.".
- 2001042161 type "text".