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＜電子ブック＞
Stability of Nonautonomous Differential Equations / by Luis Barreira, Claudia Valls
(Lecture Notes in Mathematics. ISSN:16179692 ; 1926)

版	1st ed. 2008.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2008
本文言語	英語
大きさ	XIV, 291 p : online resource
著者標目	*Barreira, Luis author Valls, Claudia author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Dynamical systems FREE:Differential Equations FREE:Dynamical Systems
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-540-74775-8

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