Selecta: Volume I: Ergodic Theory and Dynamical Systems

Hardcover | August 23, 2010

byYakov G. Sinai

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The 20 papers contained in this volume span the areas of mathematical physics, dynamical systems, and probability. Yakov Sinai is one of the most important and influential mathematicians of our time, having won the Boltzmann Medal (1986), the Dirac Medal (1992), Dannie Heinemann Prize for Mathematical Physics (1989), Nemmers Prize (2002), and the Wolf Prize in Mathematics (1997).  He is well-known as both a mathematician and a physicist, with numerous theorems and proofs bearing his name in both fields, and this book should be of interest to researchers from all fields of the physical sciences.

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The 20 papers contained in this volume span the areas of mathematical physics, dynamical systems, and probability. Yakov Sinai is one of the most important and influential mathematicians of our time, having won the Boltzmann Medal (1986), the Dirac Medal (1992), Dannie Heinemann Prize for Mathematical Physics (1989), Nemmers Prize (200...

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Format:HardcoverDimensions:466 pages, 10.24 × 7.6 × 0.27 inPublished:August 23, 2010Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387878696

ISBN - 13:9780387878690

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Table of Contents

On the notion of entropy of a dynamical system.- Construction and properties of invariant measurable partitions.- Weak isomorphism of transformations with invariant measure.- Dynamical systems with countably-multiple Lebesgue spectrum.- Dynamical systems with countably-multiple lebesgue spectrum.- Part II. Ergodic Theory and Number Theory.- Renewal-type limit theorem for the Gauss map and continued fractions.- A Limit Theorem for Birkhoff sums of non-integrable functions over rotations.- Mixing for some classes of special fl ows over rotations of the circle.- Smoothness of conjugacies of diffeomorphisms of the circle with rotations.- Feigenbaum universality and the thermodynamic formalism.- Part III. The Theory of Hyperbolic Dynamical Systems: Markov Partitions and Thermodynamic Formalism.- Markov Partitions and C diffeomorphisms.- Gibbs measures in ergodic theory.- Gibbs measures for partially hyperbolic attractors.- Steady-state electrical conduction in the periodic Lorentz gas.- Space-time chaos in the system of weakly interacting hyperbolic systems.- Part IV. Billiards.- Dynamical systems with elastic refl ections.- On a fundamental theorem in the theory of dispersing billiards.- Ergodic properties of certain systems of two-dimensional discs and three-dimensional balls.- Billiard trajectories in a polyhedral angle.

Editorial Reviews

From the reviews:"The first volume is devoted to ergodic theory and dynamical systems. It contains 19 papers divided into four groups . . The reader will find a wealth of information and ideas that can still ignite inspiration and motivate students as well as senior researchers. The reader will also have a touch of Sinai's personality, his taste, enthusiasm, and optimism, which are just as invaluable as his mathematical results." (Nikolai Chernov, Mathematical Reviews, Issue 2012 e)