Overview
- Authors:
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I. P. Cornfeld
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Landau Institute of Theoretical Physics, Academy of Sciences, Moscow, USSR
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S. V. Fomin
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Landau Institute of Theoretical Physics, Academy of Sciences, Moscow, USSR
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Ya. G. Sinai
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Landau Institute of Theoretical Physics, Academy of Sciences, Moscow, USSR
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Table of contents (16 chapters)
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Ergodicity and Mixing. Examples of Dynamical Systems
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- I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
Pages 3-42
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- I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
Pages 43-63
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- I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
Pages 64-95
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- I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
Pages 96-121
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- I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
Pages 122-137
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- I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
Pages 138-156
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- I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
Pages 157-177
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- I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
Pages 178-192
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- I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
Pages 193-224
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Basic Constructions of Ergodic Theory
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Front Matter
Pages 225-225
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- I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
Pages 227-291
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- I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
Pages 292-321
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Spectral Theory of Dynamical Systems
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Front Matter
Pages 323-323
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- I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
Pages 325-337
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- I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
Pages 338-355
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- I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
Pages 356-385
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Approximation Theory of Dynamical Systems by Periodic Dynamical Systems and Some of its Applications
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Front Matter
Pages 387-387
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- I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
Pages 389-407
About this book
Ergodic theory is one of the few branches of mathematics which has changed radically during the last two decades. Before this period, with a small number of exceptions, ergodic theory dealt primarily with averaging problems and general qualitative questions, while now it is a powerful amalgam of methods used for the analysis of statistical properties of dyna mical systems. For this reason, the problems of ergodic theory now interest not only the mathematician, but also the research worker in physics, biology, chemistry, etc. The outline of this book became clear to us nearly ten years ago but, for various reasons, its writing demanded a long period of time. The main principle, which we adhered to from the beginning, was to develop the approaches and methods or ergodic theory in the study of numerous concrete examples. Because of this, Part I of the book contains the description of various classes of dynamical systems, and their elementary analysis on the basis of the fundamental notions of ergodicity, mixing, and spectra of dynamical systems. Here, as in many other cases, the adjective" elementary" i~ not synonymous with "simple. " Part II is devoted to "abstract ergodic theory. " It includes the construc tion of direct and skew products of dynamical systems, the Rohlin-Halmos lemma, and the theory of special representations of dynamical systems with continuous time. A considerable part deals with entropy.
