{"product_id":"stability-of-nonautonomous-differential-equations-paperback","title":"Stability of Nonautonomous Differential Equations - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eLuis Barreira\u003c\/b\u003e (Author), \u003cb\u003eClaudia Valls\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003eThe 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.\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003eMain 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.\u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eLuis Barreira is a Full Professor of Mathematics at Instituto Superior T馗nico, Lisbon and a member of the Center for Mathematical Analysis, Geometry, and Dynamical Systems. He obtained his PhD from the Pennsylvania State University in 1996. In 2007 he has been awarded the Gulbenkian Science Prize. \u003c\/p\u003e\u003cp\u003eClaudia Valls is an Invited Assistant Professor at Instituto Superior T馗nico, Lisbon and a Postdoctoral Fellow at the Center for Mathematical Analysis, Geometry, and Dynamical Systems, of which she is also a member. She obtained her PhD from the Universitat de Barcelona in 1999. \u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 291\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.66 x 9.22 x 6.22 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e October 09, 2007\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":47337026257145,"sku":"9783540747741","price":89.08,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0789\/2782\/3097\/files\/7gJwpOXek49783540747741.webp?v=1769674631","url":"https:\/\/bookscloud.io\/products\/stability-of-nonautonomous-differential-equations-paperback","provider":"BooksCloud Book Dropshipping","version":"1.0","type":"link"}