000 | 03569nam a22004815i 4500 | ||
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001 | 978-3-540-74775-8 | ||
003 | DE-He213 | ||
005 | 20190213151742.0 | ||
007 | cr nn 008mamaa | ||
008 | 100301s2008 gw | s |||| 0|eng d | ||
020 |
_a9783540747758 _9978-3-540-74775-8 |
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024 | 7 |
_a10.1007/978-3-540-74775-8 _2doi |
|
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_aPBKJ _2bicssc |
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_aMAT007000 _2bisacsh |
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_aPBKJ _2thema |
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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. |
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300 |
_aXIV, 291 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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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 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-540-74775-8 |
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