Dynamical Systems and Linear Algebra

Wolfgang Kliemann, Fritz Colonius

ISBN 10: 0821883194 / ISBN 13: 9780821883198

Published by American Mathematical Society, US, 2014

About this Item

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.

Seller Inventory # LU-9780821883198

Bibliographic Details

• Title: Dynamical Systems and Linear Algebra
• Publisher: American Mathematical Society, US
• Publication Date: 2014
• Language: English
• ISBN 10: 0821883194
• ISBN 13: 9780821883198
• Binding: Hardback
• Condition: New
• Weight: 697 grams

About this title

Synopsis

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.

About the Author

Fritz Colonius, Universitat Augsburg, Germany.

Wolfgang Kliemann, Iowa State University, Ames, IA, USA.