9780821883198: Dynamical Systems and Linear Algebra
Couverture rigide
ISBN 10 : 0821883194 ISBN 13 : 9780821883198
Editeur : American Mathematical Society, 2014

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l?auteur

Fritz Colonius, Universitat Augsburg, Germany.

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

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2014
Langue
anglais
ISBN 10 
0821883194
ISBN 13 
9780821883198
Reliure
Relié
Nombre de pages
291
Coordonnées du fabricant
non disponible
Personne responsable
non disponible