# American Institute of Mathematical Sciences

August  2011, 30(3): 641-670. doi: 10.3934/dcds.2011.30.641

## Cone conditions and covering relations for topologically normally hyperbolic invariant manifolds

 1 AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland 2 Jagiellonian University, Institute of Computer Science, Łojasiewicza 6, 30-387 Kraków

Received  March 2010 Revised  October 2010 Published  March 2011

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.
Citation: Maciej J. Capiński, Piotr Zgliczyński. Cone conditions and covering relations for topologically normally hyperbolic invariant manifolds. Discrete & Continuous Dynamical Systems - A, 2011, 30 (3) : 641-670. doi: 10.3934/dcds.2011.30.641
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##### References:
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