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Paru le 10/03/2023 | Relié 249 pages
Professionnels
Stochastic properties of dynamical systems
This book provides an introduction to the study of the stochastic properties of probability preserving dynamical systems. Only the usual knowledge of the first year of a Master's degree is required. Many reminders are given. The definitions and results are illustrated by examples and corrected exercises. The book presents the notions of Poincare's recurrence, of ergodicity, of mixing. It enlights also existing links between dynamical systems and Markov chains. The final objective of this book is to present three methods for establishing central limit theorems in the context of chaotic dynamical systems : a first method based on martingale approximations, a second method based on perturbation of quasi-compact linear operators and a third method based on decorrelation estimates.
Françoise Pène studied at the University of Rennes I and after being admitted to the Agrégation of Mathematics, she did a PhD thesis under the supervision of Jean-Pierre Conze. She became maîtresse de conférences at the University of Brest. She is an honorary member of the Institut Universitaire de France and is currently university professor at the University of Brest. Her main field of research is the study of the stochastic properties of dynamical systems with chaotic behavior (including in particular the Sinai billiard, the periodic Lorentz gas, the Bunimovich stadium billiard, billiards with corners and cusps, etc.). She also works on probabilistic models (random walks in a random sceneries, etc.).
