03504nam 2200589 450 991048457850332120230829233305.03-540-74775-310.1007/978-3-540-74775-8(CKB)1000000000437246(SSID)ssj0000320177(PQKBManifestationID)11279040(PQKBTitleCode)TC0000320177(PQKBWorkID)10348250(PQKB)10472971(DE-He213)978-3-540-74775-8(MiAaPQ)EBC3062877(MiAaPQ)EBC6351797(PPN)123735912(EXLCZ)99100000000043724620210217d2008 uy 0engurnn#008mamaatxtccrStability of nonautonomous differential equations /Luis Barreira, Claudia Valls1st ed. 2008.Berlin, Germany ;New York, New York :Springer,[2008]©20081 online resource (XIV, 291 p.)Lecture notes in mathematics ;1926Bibliographic Level Mode of Issuance: Monograph3-540-74774-5 Includes bibliographical references (pages [277]-281) and index.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.Lecture Notes in Mathematics,0075-8434 ;1926Lyapunov stabilityDifferential equationsLyapunov stability.Differential equations.515.392Barreira Luís1968-0Valls Claudia1973-MiAaPQMiAaPQMiAaPQBOOK9910484578503321Stability of nonautonomous differential equations2831252UNINA