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Lecture Notes in Mathematics Ser.: Stability of Nonautonomous Differential Equations by Luis Barreira and Claudia Valls (2007, Trade Paperback)
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About this product
Product Identifiers
PublisherSpringer Berlin / Heidelberg
ISBN-103540747745
ISBN-139783540747741
eBay Product ID (ePID)63649993
Product Key Features
Number of PagesXiv, 291 Pages
Publication NameStability of Nonautonomous Differential Equations
LanguageEnglish
Publication Year2007
SubjectDifferential Equations / General, Mechanics / Dynamics, System Theory, Mathematical Analysis
TypeTextbook
Subject AreaMathematics, Science
AuthorLuis Barreira, Claudia Valls
SeriesLecture Notes in Mathematics Ser.
FormatTrade Paperback
Dimensions
Item Weight16.7 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN2007-934028
ReviewsFrom the reviews:In this book, the authors give a unified presentation of a substantial body of work which they have carried out and which revolves around the concept of nonuniform exponential dichotomy. … This is a well-written book which contains many interesting results. The reader will find significant generalizations of the standard invariant manifold theories, of the Hartman-Grobman theorem … . Anyone interested in these topics will profit from reading this book. (Russell A. Johnson, Mathematical Reviews, Issue 2010 b), From the reviews:"In this book, the authors give a unified presentation of a substantial body of work which they have carried out and which revolves around the concept of nonuniform exponential dichotomy. ... This is a well-written book which contains many interesting results. The reader will find significant generalizations of the standard invariant manifold theories, of the Hartman-Grobman theorem ... . Anyone interested in these topics will profit from reading this book." (Russell A. Johnson, Mathematical Reviews, Issue 2010 b)
Series Volume Number1926
Number of Volumes1 vol.
IllustratedYes
Table Of ContentExponential 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.
SynopsisThe main theme of this book is the stability of nonautonomous di'erential equations, with emphasis on the study of the existence and smoothness of invariant manifolds, and the Lyapunov stability of solutions. We always c- sider a nonuniform exponential behavior of the linear variational equations, given by the existence of a nonuniform exponential contraction or a nonu- form exponential dichotomy. Thus, the results hold for a much larger class of systems than in the "classical" theory of exponential dichotomies. Thedeparturepointofthebookisourjointworkontheconstructionof- variant manifolds for nonuniformly hyperbolic trajectories of nonautonomous di'erential equations in Banach spaces. We then consider several related - velopments,concerningtheexistenceandregularityoftopologicalconjugacies, the construction of center manifolds, the study of reversible and equivariant equations, and so on. The presentation is self-contained and intends to c- vey the full extent of our approach as well as its uni'ed character. The book contributes towards a rigorous mathematical foundation for the theory in the in'nite-dimensional setting, also with the hope that it may lead to further developments in the ?eld. The exposition is directed to researchers as well as graduate students interested in di'erential equations and dynamical systems, particularly in stability theory., The main theme of this book is the stability of nonautonomous di?erential equations, with emphasis on the study of the existence and smoothness of invariant manifolds, and the Lyapunov stability of solutions. We always c- sider a nonuniform exponential behavior of the linear variational equations, given by the existence of a nonuniform exponential contraction or a nonu- form exponential dichotomy. Thus, the results hold for a much larger class of systems than in the "classical" theory of exponential dichotomies. Thedeparturepointofthebookisourjointworkontheconstructionof- variant manifolds for nonuniformly hyperbolic trajectories of nonautonomous di?erential equations in Banach spaces. We then consider several related - velopments, concerningtheexistenceandregularityoftopologicalconjugacies, the construction of center manifolds, the study of reversible and equivariant equations, and so on. The presentation is self-contained and intends to c- vey the full extent of our approach as well as its uni?ed character. The book contributes towards a rigorous mathematical foundation for the theory in the in?nite-dimensional setting, also with the hope that it may lead to further developments in the ?eld. The exposition is directed to researchers as well as graduate students interested in di?erential equations and dynamical systems, particularly in stability theory., This volume covers the stability of nonautonomous differential equations in Banach spaces in the presence of nonuniform hyperbolicity. Topics under discussion include the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, and the construction and regularity of topological conjugacies. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory., The main theme of this book is the stability of nonautonomous di?erential equations, with emphasis on the study of the existence and smoothness of invariant manifolds, and the Lyapunov stability of solutions. We always c- sider a nonuniform exponential behavior of the linear variational equations, given by the existence of a nonuniform exponential contraction or a nonu- form exponential dichotomy. Thus, the results hold for a much larger class of systems than in the "classical" theory of exponential dichotomies. Thedeparturepointofthebookisourjointworkontheconstructionof- variant manifolds for nonuniformly hyperbolic trajectories of nonautonomous di?erential equations in Banach spaces. We then consider several related - velopments,concerningtheexistenceandregularityoftopologicalconjugacies, the construction of center manifolds, the study of reversible and equivariant equations, and so on. The presentation is self-contained and intends to c- vey the full extent of our approach as well as its uni?ed character. The book contributes towards a rigorous mathematical foundation for the theory in the in?nite-dimensional setting, also with the hope that it may lead to further developments in the ?eld. The exposition is directed to researchers as well as graduate students interested in di?erential equations and dynamical systems, particularly in stability theory., The main theme of this book is the stability of nonautonomous di'erential equations, with emphasis on the study of the existence and smoothness of invariant manifolds, and the Lyapunov stability of solutions. We always c- sider a nonuniform exponential behavior of the linear variational equations, given by the existence of a nonuniform exponential contraction or a nonu- form exponential dichotomy. Thus, the results hold for a much larger class of systems than in the "classical" theory of exponential dichotomies. Thedeparturepointofthebookisourjointworkontheconstructionof- variant manifolds for nonuniformly hyperbolic trajectories of nonautonomous di'erential equations in Banach spaces. We then consider several related - velopments, concerningtheexistenceandregularityoftopologicalconjugacies, the construction of center manifolds, the study of reversible and equivariant equations, and so on. The presentation is self-contained and intends to c- vey the full extent of our approach as well as its uni'ed character. The book contributes towards a rigorous mathematical foundation for the theory in the in'nite-dimensional setting, also with the hope that it may lead to further developments in the ?eld. The exposition is directed to researchers as well as graduate students interested in di'erential equations and dynamical systems, particularly in stability theory.
LC Classification NumberQA370-380
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