Stability of Nonautonomous Differential Equations / by Luis Barreira, Claudia Valls.

Format:

Book

Author/Creator:

Barreira, Luís, 1968- author.

Valls, Claudia, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1926.

Lecture Notes in Mathematics, 0075-8434 ; 1926

Language:

English

Subjects (All):

Differential equations.

Differentiable dynamical systems.

Ordinary Differential Equations.

Dynamical Systems and Ergodic Theory.

Local Subjects:

Ordinary Differential Equations.

Dynamical Systems and Ergodic Theory.

Physical Description:

1 online resource (XIV, 291 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.

System Details:

text file PDF

Summary:

Main theme of this volume is the stability of nonautonomous differential equations, with emphasis on the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, the construction and regularity of topological conjugacies, the study of center manifolds, as well as their reversibility and equivariance properties. Most results are obtained in the infinite-dimensional setting of Banach spaces. Furthermore, the linear variational equations are always assumed to possess a nonuniform exponential behavior, given either by the existence of a nonuniform exponential contraction or a nonuniform exponential dichotomy. The presentation is self-contained and has unified character. The volume contributes towards a rigorous mathematical foundation of the theory in the infinite-dimension setting, and may lead to further developments in the field. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.

Contents:

Exponential dichotomies

Exponential dichotomies and basic properties

Robustness of nonuniform exponential dichotomies

Stable manifolds and topological conjugacies

Lipschitz stable manifolds

Smooth stable manifolds in Rn

Smooth stable manifolds in Banach spaces

A nonautonomous Grobman-Hartman theorem

Center manifolds, symmetry and reversibility

Center manifolds in Banach spaces

Reversibility and equivariance in center manifolds

Lyapunov regularity and stability theory

Lyapunov regularity and exponential dichotomies

Lyapunov regularity in Hilbert spaces

Stability of nonautonomous equations in Hilbert spaces.

Other Format:

Printed edition:

ISBN:

9783540747758

Access Restriction:

Restricted for use by site license.