02745nam a2200373 i 4500991000160479707536031204s2001 de a b 001 0 eng d3110169916b12578277-39ule_instDip.to Matematicaeng515.35221AMS 37-01AMS 37A50AMS 37A30AMS 70K55LC QA614.8.B4853.1.65Berger, Arno481526Chaos and chance :an introduction to stochastic aspects of dynamics /Arno BergerBerlin ; New York :Walter de Gruyter,2001x, 245 p. :ill. ;24 cmDe Gruyter textbookIncludes bibliographical references (p. [237]-240) and indexIntroduction. 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 triangleDifferentiable dynamical systemsChaotic behavior in systemsTable of contentshttp://www.loc.gov/catdir/toc/fy031/2001042161.htmlTable of contents.b1257827712-10-1204-12-03991000160479707536LE006 53.1.65 BER12006000154277le006pE34.56-l- 00000.i1399474831-01-05LE013 37-XX BER11 (2001)12013000143637le013pE52.98-l- 02020.i1307597410-02-04Chaos and chance254054UNISALENTOle006(2)le01304-12-03ma -engde 03