Stability of nonautonomous differential equations

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 r...

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Bibliographic Details
Main Author: Barreira, Luís, 1968-
Corporate Author: SpringerLink (Online service)
Other Authors: Valls, Claudia
Format: eBook
Language:English
Published: Berlin ; New York : Springer, ©2008.
Berlin ; New York : [2008]
Series:Lecture notes in mathematics (Springer-Verlag) ; 1926.
Physical Description:
1 online resource (xiv, 285 pages) : illustrations.
Subjects:
Lyapunov stability.
Differential equations.
Stability.
Manifolds (Mathematics)
Online Access:SpringerLink - Click here for access

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245 1 0 |a Stability of nonautonomous differential equations /  |c Luis Barreira, Claudia Valls. 
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504 |a Includes bibliographical references (pages 277-281) and index. 
505 0 |a Exponential dichotomies and basic properties -- Robustness of nonuniform exponential dichotomies -- Lipschitz stable manifolds -- Smooth stable manifolds in Banach spaces -- A nonautonomous Grobman-Hartman theorem -- Center manifolds in Banach spaces -- Reversibility and equivariance in center manifolds -- Lyapunov regularity and exponential dichotomies -- Lyapunov regularity in Hilbert spaces -- Stability of nonautonomous equations in Hilbert spaces. 
588 0 |a Print version record. 
520 |a 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. 
546 |a English. 
650 0 |a Lyapunov stability.  |0 https://id.loc.gov/authorities/subjects/sh95003362. 
650 0 |a Differential equations.  |0 https://id.loc.gov/authorities/subjects/sh85037890. 
650 0 |a Stability.  |0 https://id.loc.gov/authorities/subjects/sh85127185. 
650 0 |a Manifolds (Mathematics)  |0 https://id.loc.gov/authorities/subjects/sh85080549. 
650 6 |a Équations différentielles. 
650 6 |a Stabilité. 
650 6 |a Variétés (Mathématiques) 
650 6 |a Stabilité au sens de Liapounov. 
650 7 |a stability.  |2 aat. 
650 7 |a Variedades (Matemáticas)  |2 embne. 
650 7 |a Estabilidad.  |2 embne. 
650 7 |a Ecuaciones diferenciales.  |2 embne. 
650 7 |a Stability.  |2 fast. 
650 7 |a Manifolds (Mathematics)  |2 fast. 
650 7 |a Differential equations.  |2 fast. 
650 7 |a Lyapunov stability.  |2 fast. 
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