Abstract
The persistence of a (compact) normally hyperbolic manifold and the existence of its stable and unstable manifolds, corresponding to the action of C r maps or semiflows, r ≥ 1, are well known facts (see, for instance, [102] and [176]). The more general case of (compact) hyperbolic sets that are invariant under (not necessarily injective) maps was also carefully studied (see Ruelle [176], Shub [189] and Palis and Takens [163]). The persistence and smoothness of (compact) hyperbolic invariant manifolds for RFDE were considered in detail in Magalhães [132] based on skew-product semiflows defined for RFDE, locally around hyperbolic invariant manifolds, and their spectral properties, associated with exponential dichotomies, following the lines of work developed by Sacker and Sell for flows([186], [187]).
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© 2002 Springer Science+Business Media New York
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Hale, J.K., Magalhães, L.T., Oliva, W.M. (2002). One-to-Oneness, Persistence, and Hyperbolicity. In: Dynamics in Infinite Dimensions. Applied Mathematical Sciences, vol 47. Springer, New York, NY. https://doi.org/10.1007/0-387-22896-9_7
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DOI: https://doi.org/10.1007/0-387-22896-9_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3012-5
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