Topological Dynamics and Applications

Erscheinungsjahr 1997
ISBN: 978-0-8218-0608-1
Verlag: American Mathematical Society

Buch, Englisch, 334 Seiten, Gewicht: 641 g

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 Furstenburg 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. 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 non-autonomous linear differential equations are shown. Exposition on recent results about Floquet theory, bifurcation theory and Lyapanov exponents is given.

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.

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen