Stability of Nonautonomous Differential Equations

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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Détails bibliographiques
Auteurs principaux : Barreira Luis (Auteur), Valls Claudia (Auteur)
Format : Livre
Langue : anglais
Titre complet : Stability of Nonautonomous Differential Equations / Luis Barreira, Claudia Valls.
Publié : Berlin, Heidelberg : Springer Berlin Heidelberg , 2008
Springer e-books
Collection : Lecture notes in mathematics (Internet) ; 1926
Titre de l'ensemble : Lecture Notes in Mathematics vol. 1926
Disponibilité : L'accès complet au document est réservé aux usagers des établissements qui en ont fait l'acquisition
Contenu : 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
Sujets :
Équations différentielles
Théorie ergodique
Mathématiques
Mathematics
Ordinary Differential Equations
Dynamical Systems and Ergodic Theory
Documents associés : Autre format: Stability of nonautonomous differential equations
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320 |a Bibliogr. Index 
327 1 |a Exponential dichotomies  |a Exponential dichotomies and basic properties  |a Robustness of nonuniform exponential dichotomies  |a Stable manifolds and topological conjugacies  |a Lipschitz stable manifolds  |a Smooth stable manifolds in Rn  |a Smooth stable manifolds in Banach spaces  |a A nonautonomous Grobman Hartman theorem  |a Center manifolds, symmetry and reversibility  |a Center manifolds in Banach spaces  |a Reversibility and equivariance in center manifolds  |a Lyapunov regularity and stability theory  |a Lyapunov regularity and exponential dichotomies  |a Lyapunov regularity in Hilbert spaces  |a Stability of nonautonomous equations in Hilbert spaces 
330 |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 
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