
Introduction  Preview Material  Table of Contents  Index  Supplementary Material 
Graduate Studies in Mathematics 2014; 284 pp; hardcover Volume: 158 ISBN10: 0821883194 ISBN13: 9780821883198 List Price: US$67 Member Price: US$53.60 Order Code: GSM/158 See also: Recurrence and Topology  John M Alongi and Gail S Nelson Dynamical Systems and Population Persistence  Hal L Smith and Horst R Thieme Nonautonomous Dynamical Systems  Peter E Kloeden and Martin Rasmussen  This book provides an introduction to the interplay between linear algebra and dynamical systems in continuous time and in discrete time. It first reviews the autonomous case for one matrix \(A\) via induced dynamical systems in \(\mathbb{R}^d\) and on Grassmannian manifolds. Then the main nonautonomous approaches are presented for which the time dependency of \(A(t)\) is given via skewproduct flows using periodicity, or topological (chain recurrence) or ergodic properties (invariant measures). The authors develop generalizations of (real parts of) eigenvalues and eigenspaces as a starting point for a linear algebra for classes of timevarying linear systems, namely periodic, random, and perturbed (or controlled) systems. The book presents for the first time in one volume a unified approach via Lyapunov exponents to detailed proofs of Floquet theory, of the properties of the Morse spectrum, and of the multiplicative ergodic theorem for products of random matrices. The main tools, chain recurrence and Morse decompositions, as well as classical ergodic theory are introduced in a way that makes the entire material accessible for beginning graduate students. Readership Graduate students and research mathematicians interested in matrices and random dynamical systems. 


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