Topics in Dynamics and Ergodic Theory (London Mathematical Society Lecture Note Series, Series Number 310)

This Book Contains A Collection Of Survey Papers By Leading Researchers In Ergodic Theory, Low-dimensional And Topological Dynamics And It Comprises Nine Chapters On A Range Of Important Topics. These Include: The Role And Usefulness Of Ultrafilters In Ergodic Theory, Topological Dynamics And Ramsey Theory; Topological Aspects Of Kneading Theory Together With An Analogous 2-dimensional Theory Called Pruning; The Dynamics Of Markov Odometers, Bratteli-vershik Diagrams And Orbit Equivalence Of Non-singular Automorphisms; Geometric Proofs Of Mather's Connecting And Accelerating Theorems; Recent Results In One Dimensional Smooth Dynamics; Periodic Points Of Nonexpansive Maps; Arithmetic Dynamics; The Defect Of Factor Maps; Entropy Theory For Actions Of Countable Amenable Groups. Sergey Bezuglyi, Sergiy Kolyada. Includes Bibliographical References And Index. This collection of survey papers by leading researchers in ergodic theory and low-dimensional and topological dynamics comprises nine chapters on a range of important topics. These include: the role and usefulness of ultrafilters in ergodic theory, topological dynamics and Ramsey theory; topological aspects of kneading theory together with an analogous 2-dimensional theory called pruning; the dynamics of Markov odometers, Bratteli-Vershik diagrams and orbit equivalence of non-singular automorphisms; geometric proofs of Mather's connecting and accelerating theorems; recent results in one dimensional smooth dynamics; periodic points of nonexpansive maps; arithmetic dynamics; the defect of factor maps; entropy theory for actions of countable amenable groups. Dear colleagues and friends! This conference is devoted to the memory of Vladimir Mikhaylovich Alexeyev, professor of the Moscow State University, who untimely passed away in 1980.