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Journal of Mathematical Physics / Volume 53 / Issue 2 / ARTICLES / Dynamical Systems

J. Math. Phys. 53, 022702 (2012); http://dx.doi.org/10.1063/1.3683233 (7 pages)

Total destruction of invariant tori for the generalized Frenkel–Kontorova model

Xifeng Su1 and Lin Wang2

1Academy of Mathematics and Systems Science, Chinese Academy of Sciences, No. 55 Zhongguancun East Road, Beijing 100190, China
2Department of Mathematics, Nanjing University, 22 Hankou Road, Nanjing 210093, China

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(Received 29 November 2011; accepted 13 January 2012; published online 13 February 2012)

We consider generalized Frenkel–Kontorova models on higher dimensional lattices. We show that the invariant tori which are parameterized by continuous hull functions can be destroyed by small perturbations in the Cr topology with r < 1.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. COMPARISON WITH THE LITERATURES
  3. PRELIMINARIES
  4. A VARIATIONAL CRITERION OF TOTAL DESTRUCTION OF INVARIANT TORI
  5. PROOF OF THEOREM 1
    1. Construction of the generalized Frenkel–Kontorova models
    2. Total destruction of invariant tori

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KEYWORDS and PACS

Keywords

lattice theory, topology

PACS

  • 05.50.+q

    Lattice theory and statistics (Ising, Potts, etc.)

  • 02.40.Pc

    General topology

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3683233

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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