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http://hdl.handle.net/2445/33852
Title: | Reliable computation of robust response tori on the verge of breakdown |
Author: | Figueras Romero, Jordi-Lluís Haro, Àlex |
Keywords: | Dinàmica Invariants Dynamics Invariants |
Issue Date: | 12-Apr-2012 |
Publisher: | Society for Industrial and Applied Mathematics |
Abstract: | We prove the existence and local uniqueness of invariant tori on the verge of breakdown for two systems: the quasi-periodically driven logistic map and the quasi-periodically forced standard map. These systems exemplify two scenarios: the Heagy-Hammel route for the creation of strange non- chaotic attractors and the nonsmooth bifurcation of saddle invariant tori. Our proofs are computer- assisted and are based on a tailored version of the Newton-Kantorovich theorem. The proofs cannot be performed using classical perturbation theory because the two scenarios are very far from the perturbative regime, and fundamental hypotheses such as reducibility or hyperbolicity either do not hold or are very close to failing. Our proofs are based on a reliable computation of the invariant tori and a careful study of their dynamical properties, leading to the rigorous validation of the numerical results with our novel computational techniques. |
Note: | Reproducció del document publicat a: http://dx.doi.org/10.1137/100809222 |
It is part of: | SIAM Journal On Applied Dynamical Systems, 2012, vol. 11, num. 2, p. 597-628 |
URI: | http://hdl.handle.net/2445/33852 |
Related resource: | http://dx.doi.org/10.1137/100809222 |
ISSN: | 1536-0040 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
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606390.pdf | 2.9 MB | Adobe PDF | View/Open |
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