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Dynamical Systems of Algebraic Origin (Modern Birkh User Classics)by Klaus Schmidt
Synopses & ReviewsPublisher Comments:Although much of classical ergodic theory is concerned with single transformations and oneparameter flows, the subject inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multidimensional symmetry groups. However, the wealth of concrete and natural examples which has contributed so much to the appeal and development of classical dynamics, is noticeably absent in this more general theory. The purpose of this book is to help remedy this scarcity of explicit examples by introducing a
Synopsis:This book introduces a class of continuous Zdactions diverse enough to exhibit many of the new phenomena encountered in the transition from Z to Zd, but which lends itself to systematic study: the Zdactions by automorphisms of compact, abelian groups.
Synopsis:Although much of classical ergodic theory is concerned with single transformations and oneparameter flows, the subject inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multidimensional symmetry groups. However, the wealth of concrete and natural examples which has contributed so much to the appeal and development of classical dynamics, is noticeably absent in this more general theory. The purpose of this book is to help remedy this scarcity of explicit examples by introducing a
About the AuthorKlaus Schmidt is a Professor of Mathematics at the University of Vienna, Austria.
Table of ContentsIntroduction. Chapter I. Group actions by automorphisms fo compact groups. Chapter II. Zdactions on compact abelian groups. Chapter III. Expansive automorphisms of compact groups. Chapter IV. Periodic points. Chapter V. Entropy. Chapter VI. Positive entropy. Chapter VII. Zero entropy. Chapter VIII. Mixing. Chapter IX. Rigidity. Bibliography. Index.
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Science and Mathematics » Mathematics » Algebra » Abstract Algebra


