Result: Computer assisted proof for normally hyperbolic invariant manifolds
Title:
Computer assisted proof for normally hyperbolic invariant manifolds
Authors:
Source:
Nonlinearity (Bristol. Print). 25(7):1997-2026
Publisher Information:
Bristol: Institute of Physics, 2012.
Publication Year:
2012
Physical Description:
print, 22 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Fonctions de plusieurs variables complexes et espaces analytiques, Several complex variables and analytic spaces, Equations différentielles, Ordinary differential equations, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Divers, Other topics in mathematical methods in physics, Analyse intervalle, Interval analysis, análisis intervalo, Analyse non linéaire, Nonlinear analysis, análisis no lineal, Analyse numérique, Numerical analysis, Análisis numérico, Application logistique, Logistic map, Aplicación logística, Attracteur chaotique, Chaotic attractor, Atractor caótico, Ordinateur, Computer, Computadora, Perturbation, Perturbación, Physique mathématique, Mathematical physics, Física matemática, Simulation numérique, Numerical simulation, Simulación numérica, Variété invariante, Invariant manifold, Variedad invariante, Vérification, Verification, Verificación, 32Q45, 34K19, 37D10, 65G40, 65Gxx, 65J05, 65Jxx, Attracteur hyperbolique, Courbe invariante, Invariant curve, Variété hyperbolique
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
Faculty of Applied Mathematics, AGH University of Science and Technology, Mickiewicza 30, 30-059 Kraków, Poland
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
ISSN:
0951-7715
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Theoretical physics
Theoretical physics
Accession Number:
edscal.26131761
Database:
PASCAL Archive
Further Information
We present a topological proof of the existence of a normally hyperbolic invariant manifold for maps. 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. But a non-rigorous, good enough, guess is necessary. The required assumptions are formulated in a way which allows for an 'a posteriori' verification by rigorous-interval-based numerical analysis. We apply our method for a driven logistic map, for which non-rigorous numerical simulation in plain double precision suggests the existence of a chaotic attractor. We prove that this numerical evidence is false and that the attractor is a normally hyperbolic invariant curve.