Topological Dynamics and Applications (Contemporary Mathematics)

Topological Dynamics and Applications (Contemporary Mathematics)

By: M. G. Nerurkar (author), D. G. Ellis (editor), D. P. Dokken (editor), M. G. Nerurkar (editor)Paperback

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Description

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: 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 almost-periodicity, hidden eigenvalues, a natural family of factors and topological analogues of ergodic decomposition); 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; and, applications to non-autonomous linear differential equations are shown. Exposition on recent results about Floquet theory, bifurcation theory and Lyapanov exponents is given.

Contents

Part I. Topological Dynamics: Abstract Theory: Robert Ellis and the algebra of dynamical systems by H. Furstenberg and E. Glasner Weak mixing and pure weak mixing minimal flows by J. Auslander A natural family of factors for minimal flows by E. Glasner, M. Mentzen, and A. Siemaszko Topological ergodic decomposition and homogeneous flows by E. Akin and E. Glasner On the proximal and regionally proximal relation of an extension between minimal flows by D. Penazzi Almost equicontinuity and the enveloping semigroup by E. Akin, J. Auslander, and K. Berg Some universal constructions in abstract topological dynamics by V. Pestov Weakly almost periodic flows and hidden eigenvalues by T. Downarowicz Enveloping linear maps by E. Akin An overview of the construction of suspension flows using continuous cocycles by H. Keynes, K. Madden, N. Markley, and M. Sears Suspensions, inheritance, and flows on homogeneous spaces by D. Ellis On the lifting of transformation semigroups by H. Ikeshoji and T. Wu Part II. Applications and Other Dynamical Results: Idempotent measures associated to a locally compact topological group by D. Dokken Another proof of Moore's ergodicity theorem for $SL(2,\mathbb{R})$ by S. Adams Multiple recurrence and doubly minimal systems by B. Weiss Subset dynamics and van der Waerden's theorem by H. Furstenberg and E. Glasner Recurrence for semigroup actions and a non-commutative Schur theorem by V. Bergelson and R. McCutcheon A note on Livsic's periodic point theorem by Z. Coelho, W. Parry, and R. Williams A zero-one law for dynamical properties by E. Glasner and J. L. King Residuality and orbit equivalence by D. Rudolph Uncountably many Vershik-inequivalent group actions of equal entropy by J. Feldman Part III. Applications to Differential Equations: Positive exponents for a dense set of continuous $SL(2, {\mathbfR})$ valued cocycles which arise as solutions to strongly accessible linear differential systems by M. Nerurkar Topological dynamics and differential equations by G. Sell, W. Shen, and Y. Yi An ergodic and topological approach to almost periodic bidimensional linear systems by S. Novo and R. Obaya An application of topological dynamics to bifurcation theory by R. Johnson.

Product Details

  • ISBN13: 9780821806081
  • Format: Paperback
  • Number Of Pages: 334
  • ID: 9780821806081
  • ISBN10: 0821806084

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