الصفحة 1
الصفحة 1
Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms
For this printing of R. Bowen's book, J.-R. Chazottes has retyped it in TeX for easier reading, thereby correcting typos and bibliographic details. From the Preface by D. Ruelle: "Rufus Bowen has left us a masterpiece of mathematical exposition... Here a number of results which were new at the time are presented in such a clear and lucid style that Bowen's monograph immediately became a classic. More than thirty years later, many new results have been proved in this area, but the volume is as useful as ever because it remains the best introduction to the basics of the ergodic theory of hyperbolic systems."
Elliptic Theory and Noncommutative Geometry : Nonlocal Elliptic Operators
This comprehensive yet concise book deals with nonlocal elliptic differential operators, whose coefficients involve shifts generated by diffeomorophisms of the manifold on which the operators are defined. The main goal of the study is to relate analytical invariants (in particular, the index) of such elliptic operators to topological invariants of the manifold itself. This problem can be solved by modern methods of noncommutative geometry. This is the first and so far the only book featuring a consistent application of methods of noncommutative geometry to the index problem in the theory of nonlocal elliptic operators. Although the book provides important results, which are in a sense definitive, on the above-mentioned topic, it contains all the necessary preliminary material, such as C*-algebras and their K-theory or cyclic homology.
Dynamics beyond uniform hyperbolicity : A global geometric and probabilistic perspective
In broad terms, the goal of dynamics is to describe the long-term evolution of systems for which an ""infinitesimal"" evolution rule, such as a differential equation or the iteration of a map, is known.This book aims to put such recent developments in a unified perspective, and to point out open problems and likely directions for further progress. It is aimed willing to get a quick, yet broad, view of this part of dynamics. Main ideas, methods, and results are discussed, at variable degrees of depth, with references to the original works for details and complementary information.
