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020 _a9783540747758
_9978-3-540-74775-8
024 7 _a10.1007/978-3-540-74775-8
_2doi
050 4 _aQA372
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
072 7 _aPBKJ
_2thema
082 0 4 _a515.352
_223
100 1 _aBarreira, Luis.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aStability of Nonautonomous Differential Equations
_h[electronic resource] /
_cby Luis Barreira, Claudia Valls.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2008.
300 _aXIV, 291 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1926
505 0 _aExponential 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.
520 _aMain 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.
650 0 _aDifferential Equations.
650 0 _aDifferentiable dynamical systems.
650 1 4 _aOrdinary Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12147
650 2 4 _aDynamical Systems and Ergodic Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M1204X
700 1 _aValls, Claudia.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540843481
776 0 8 _iPrinted edition:
_z9783540747741
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1926
856 4 0 _uhttps://doi.org/10.1007/978-3-540-74775-8
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c11765
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