Contemporary Mathematics 1998; 334 pp; softcover Volume: 215 ISBN10: 0821806084 ISBN13: 9780821806081 List Price: US$89 Member Price: US$71.20 Order Code: CONM/215
 This book is a very readable exposition of the modern theory of topological dynamics and presents diverse applications to such areas as ergodic theory, combinatorial number theory and differential equations. There are three parts: 1) The abstract theory of topological dynamics is discussed, including a comprehensive survey by Furstenberg and Glasner on the work and influence of R. Ellis. Presented in book form for the first time are new topics in the theory of dynamical systems, such as weak almostperiodicity, hidden eigenvalues, a natural family of factors and topological analogues of ergodic decomposition. 2) The power of abstract techniques is demonstrated by giving a very wide range of applications to areas of ergodic theory, combinatorial number theory, random walks on groups and others. 3) Applications to nonautonomous linear differential equations are shown. Exposition on recent results about Floquet theory, bifurcation theory and Lyapanov exponents is given. Readership Graduate students and research mathematicians working in ergodic theory, topological dynamics, differential equations and dynamical systems. Table of Contents Part I. Topological Dynamics: Abstract Theory  H. Furstenberg and E. Glasner  Robert Ellis and the algebra of dynamical systems
 J. Auslander  Weak mixing and pure weak mixing minimal flows
 E. Glasner, M. Mentzen, and A. Siemaszko  A natural family of factors for minimal flows
 E. Akin and E. Glasner  Topological ergodic decomposition and homogeneous flows
 D. Penazzi  On the proximal and regionally proximal relation of an extension between minimal flows
 E. Akin, J. Auslander, and K. Berg  Almost equicontinuity and the enveloping semigroup
 V. Pestov  Some universal constructions in abstract topological dynamics
 T. Downarowicz  Weakly almost periodic flows and hidden eigenvalues
 E. Akin  Enveloping linear maps
 H. Keynes, K. Madden, N. Markley, and M. Sears  An overview of the construction of suspension flows using continuous cocycles
 D. Ellis  Suspensions, inheritance, and flows on homogeneous spaces
 H. Ikeshoji and T. Wu  On the lifting of transformation semigroups
Part II. Applications and Other Dynamical Results  D. Dokken  Idempotent measures associated to a locally compact topological group
 S. Adams  Another proof of Moore's ergodicity theorem for \(SL(2,\mathbb{R})\)
 B. Weiss  Multiple recurrence and doubly minimal systems
 H. Furstenberg and E. Glasner  Subset dynamics and van der Waerden's theorem
 V. Bergelson and R. McCutcheon  Recurrence for semigroup actions and a noncommutative Schur theorem
 Z. Coelho, W. Parry, and R. Williams  A note on Livšic's periodic point theorem
 E. Glasner and J. L. King  A zeroone law for dynamical properties
 D. Rudolph  Residuality and orbit equivalence
 J. Feldman  Uncountably many Vershikinequivalent group actions of equal entropy
Part III. Applications to Differential Equations  M. Nerurkar  Positive exponents for a dense set of continuous \(SL(2, {\mathbf R})\) valued cocycles which arise as solutions to strongly accessible linear differential systems
 G. Sell, W. Shen, and Y. Yi  Topological dynamics and differential equations
 S. Novo and R. Obaya  An ergodic and topological approach to almost periodic bidimensional linear systems
 R. Johnson  An application of topological dynamics to bifurcation theory
