Please use this identifier to cite or link to this item: 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
Related resource: http://dx.doi.org/10.1137/100809222
URI: http://hdl.handle.net/2445/33852
ISSN: 1536-0040
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

Files in This Item:
File Description SizeFormat 
606390.pdf2.9 MBAdobe PDFView/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.