Cone Conditions and Covering Relations for Topologically Normally Hyperbolic Invariant Manifolds

2011/03/10 by Maciej J. Capiński, Maciej J Capinski, Piotr Zgliczyński +3
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS

paper · pdf · doi:10.48550/arxiv.1103.1959

arxiv created 2011/03/10 · openalex publication_date 2011/03/10 · arxiv updated 2011/03/11 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We present a topological proof of the existence of invariant manifolds for maps with normally hyperbolic-like properties. The proof is conducted in the phase space of the system. In our approach we do not require that the map is a perturbation of some other map for which we already have an invariant manifold. We provide conditions which imply the existence of the manifold within an investigated region of the phase space. The required assumptions are formulated in a way which allows for rigorous computer assisted verification. We apply our method to obtain an invariant manifold within an explicit range of parameters for the rotating Hénon map.

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