
Dynamical Systems and Linear Algebra
American Mathematical Society (Publisher)
Published on 30. October 2014
Book
Hardback
291 pages
978-0-8218-8319-8 (ISBN)
Description
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 {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.
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.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
College/higher education
Dimensions
Height: 254 mm
Width: 178 mm
Weight
697 gr
ISBN-13
978-0-8218-8319-8 (9780821883198)
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Schweitzer Classification
Persons
Fritz Colonius, Universitat Augsburg, Germany.
Wolfgang Kliemann, Iowa State University, Ames, IA, USA.
Wolfgang Kliemann, Iowa State University, Ames, IA, USA.