Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders View Full Text


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Article Info

DATE

2016-09

AUTHORS

Patrick Bernard, Vadim Kaloshin, Ke Zhang

ABSTRACT

We prove a form of Arnold diffusion in the a-priori stable case. Let H0(p)+ϵH1(θ,p,t),θ∈Tn,p∈Bn,t∈T=R/T,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{0}(p)+\epsilon H_{1}(\theta,p,t),\quad \theta \in {\mathbb{T}^{n}},\,p \in B^{n},\,t \in \mathbb{T}= \mathbb{R}/\mathbb{T},$$\end{document}be a nearly integrable system of arbitrary degrees of freedom n⩾2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${n \geqslant 2}$$\end{document} with a strictly convex H0. We show that for a “generic” ϵH1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\epsilon H_1}$$\end{document}, there exists an orbit (θ,p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(\theta,p)}$$\end{document} satisfying ‖p(t)-p(0)‖>l(H1)>0,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\|p(t)-p(0)\| > l(H_{1}) > 0,$$\end{document}where l(H1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${l(H_1)}$$\end{document} is independent of ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\epsilon}$$\end{document}. The diffusion orbit travels along a codimension-1 resonance, and the only obstruction to our construction is a finite set of additional resonances.For the proof we use a combination of geometric and variational methods, and manage to adapt tools which have recently been developed in the a-priori unstable case. More... »

PAGES

1-79

References to SciGraph publications

  • 1999-08. Minimal Measures and Minimizing Closed Normal One-currents in GEOMETRIC AND FUNCTIONAL ANALYSIS
  • 2011-03-03. Speed of Arnold diffusion for analytic Hamiltonian systems in INVENTIONES MATHEMATICAE
  • 1989-12. KAM theory in configuration space in COMMENTARII MATHEMATICI HELVETICI
  • 2012-09-18. An Example of a Nearly Integrable Hamiltonian System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2003-10-06. Existence of C1 critical subsolutions of the Hamilton-Jacobi equation in INVENTIONES MATHEMATICAE
  • 2008-01-01. Geometric approaches to the problem of instability in Hamiltonian systems. An informal presentation in HAMILTONIAN DYNAMICAL SYSTEMS AND APPLICATIONS
  • 2004-12. Arnold Diffusion. I: Announcement of Results in JOURNAL OF MATHEMATICAL SCIENCES
  • 2010-10-17. Large Normally Hyperbolic Cylinders in a priori Stable Hamiltonian Systems in ANNALES HENRI POINCARÉ
  • 1973. The stable manifold theorem via an isolating block in SYMPOSIUM ON ORDINARY DIFFERENTIAL EQUATIONS
  • 2010-03-31. Variational construction of unbounded orbits in Lagrangian systems in SCIENCE CHINA MATHEMATICS
  • 2002-04. Multidimensional Symplectic Separatrix Maps in JOURNAL OF NONLINEAR SCIENCE
  • 2003-05. Stability and instability for Gevrey quasi-convex near-integrable Hamiltonian systems in PUBLICATIONS MATHÉMATIQUES DE L'IHÉS
  • 2010-01-16. On the Number of Mather Measures of Lagrangian Systems in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
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    19 schema:description We prove a form of Arnold diffusion in the a-priori stable case. Let H0(p)+ϵH1(θ,p,t),θ∈Tn,p∈Bn,t∈T=R/T,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{0}(p)+\epsilon H_{1}(\theta,p,t),\quad \theta \in {\mathbb{T}^{n}},\,p \in B^{n},\,t \in \mathbb{T}= \mathbb{R}/\mathbb{T},$$\end{document}be a nearly integrable system of arbitrary degrees of freedom n⩾2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${n \geqslant 2}$$\end{document} with a strictly convex H0. We show that for a “generic” ϵH1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\epsilon H_1}$$\end{document}, there exists an orbit (θ,p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(\theta,p)}$$\end{document} satisfying ‖p(t)-p(0)‖>l(H1)>0,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\|p(t)-p(0)\| > l(H_{1}) > 0,$$\end{document}where l(H1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${l(H_1)}$$\end{document} is independent of ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\epsilon}$$\end{document}. The diffusion orbit travels along a codimension-1 resonance, and the only obstruction to our construction is a finite set of additional resonances.For the proof we use a combination of geometric and variational methods, and manage to adapt tools which have recently been developed in the a-priori unstable case.
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