Geometric proof for normally hyperbolic invariant manifolds
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Publication:496743
DOI10.1016/J.JDE.2015.07.020zbMath1352.37077arXiv1503.03323OpenAlexW2964306459MaRDI QIDQ496743
Maciej J. Capiński, Piotr Zgliczyński
Publication date: 22 September 2015
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1503.03323
Invariant manifold theory for dynamical systems (37D10) Invariant manifolds for ordinary differential equations (34C45) Stability of manifolds of solutions to ordinary differential equations (34D35)
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Cites Work
- Unnamed Item
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- Unnamed Item
- Cone conditions and covering relations for topologically normally hyperbolic invariant manifolds
- A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: rigorous results
- Approximately invariant manifolds and global dynamics of spike states
- Covering relations and the existence of topologically normally hyperbolic invariant sets
- Covering relations, cone conditions and the stable manifold theorem
- Construction of invariant whiskered tori by a parameterization method. I: Maps and flows in finite dimensions
- Normally hyperbolic invariant manifolds in dynamical systems
- A KAM theory for conformally symplectic systems: efficient algorithms and their validation
- Computer assisted proof for normally hyperbolic invariant manifolds
- Reliable Computation of Robust Response Tori on the Verge of Breakdown
- Uniformly Hyperbolic Attractor of the Smale–Williams Type for a Poincaré Map in the Kuznetsov System
- Differential Topology
- Asymptotic stability with rate conditions for dynamical systems
- Stable manifolds and the Perron–Irwin method
- A Parameterization Method for the Computation of Invariant Tori and Their Whiskers in Quasi‐Periodic Maps: Explorations and Mechanisms for the Breakdown of Hyperbolicity
- Existence of a Center Manifold in a Practical Domain around $L_1$ in the Restricted Three-Body Problem
- A geometrical proof of the persistence of normally hyperbolic submanifolds
- Invariant manifolds
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