Selecta I

The 20 papers in this volume span mathematical physics, dynamical systems, and probability. Yakov Sinai is one of the most important and influential mathematicians of our time; this book will interest researchers from all fields of the physical sciences.

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)

Brilliant and unconventional ideas With commentaries by Y. Sinai for each paper Extensive collection of seminal papers by the author Includes supplementary material: sn.pub/extras

Klappentext

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)

Inhalt
Entropy Theory of Dynamical systems.- 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. I.- Dynamical Systems with Countably-Multiple Lebesgue Spectrum. 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 Flows Over Rotations of the Circle.- Smoothness of conjugacies of diffeomorphisms of the circle with rotations.- Feigenbaum universality and the thermodynamic formalism.- 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.- Billiards.- Dynamical Systems with Elastic Reflections.- 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.