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- W3111263636 abstract "It was proved that both the normal hyperbolicity and invariant manifold for a uniformly hyperbolic compact invariant manifold and the invariant manifold for a uniformly hyperbolic noncompact invariant manifold are persistent under small perturbation. In this paper, we weaken the uniform normal hyperbolicity to the nonuniform one and prove that both the nonuniform normal hyperbolicity and invariant manifold for a nonuniformly eventually absolutely normally hyperbolic noncompact invariant manifold are persistent under small perturbation in Banach spaces. Unlike the uniform case, we need infinitely many families of norms to uniformize infinitely many exponential dichotomies correspondingly. We use the approximative exponential dichotomy and the pseudo orbit to overcome the difficulty." @default.
- W3111263636 created "2020-12-21" @default.
- W3111263636 creator A5019414664 @default.
- W3111263636 creator A5050379145 @default.
- W3111263636 date "2021-02-01" @default.
- W3111263636 modified "2023-10-18" @default.
- W3111263636 title "Approximative dichotomy and persistence of nonuniformly normally hyperbolic invariant manifolds in Banach spaces" @default.
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- W3111263636 doi "https://doi.org/10.1016/j.jde.2020.12.001" @default.
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