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Dynamical Systems and Linear Algebra
Fritz Colonius, Universität Augsburg, Germany, and Wolfgang Kliemann, Iowa State University, Ames, IA
cover
Graduate Studies in Mathematics
2014; 284 pp; hardcover
Volume: 158
ISBN-10: 0-8218-8319-4
ISBN-13: 978-0-8218-8319-8
List Price: US$67
Member Price: US$53.60
Order Code: GSM/158
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Not yet published.
Expected publication date is October 14, 2014.
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 skew-product 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 time-varying 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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