On diffusion in high-dimensional Hamiltonian systems

  title={On diffusion in high-dimensional Hamiltonian systems},
  author={Jean Bourgaina and Vadim Kaloshinb},
  • Jean Bourgaina, Vadim Kaloshinb
  • Published 2005
The purpose of this paper is to construct examples of diffusion for -Hamiltonian perturbations of completely integrable Hamiltonian systems in 2d-dimensional phase space, with d large. In the first part of the paper, simple and explicit examples are constructed illustrating absence of ‘long-time’ stability for size Hamiltonian perturbations of quasi-convex integrable systems already when the dimension 2d of phase space becomes as large as log 1 . We first produce the example in Gevrey class and… CONTINUE READING
Highly Cited
This paper has 31 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.


Publications referenced by this paper.
Showing 1-10 of 20 references

Variational construction of trajectories for time periodic Lagrangian systems on the two torus

  • J. Mather
  • 1996
Highly Influential
3 Excerpts

Diffusion, I: Announcement of results, Kluwer Academic Plenum Publication Series, Dordrecht, Math

  • J. Mather, Arnold
  • 2004

Arnold diffusion and instabilities in Hamiltonian dynamics, preprint, 2002, 34pp

  • Z. Xia
  • 2002


  • Ch. Golé, Symplectic Twist Maps, Global Variational Techniques, Advanced Series in Nonlinear Dynamics
  • 18,
  • 2001

On diffusion in high-dimensional Hamiltonian systems and PDE

  • J. Bourgain
  • J. Analyse Math
  • 2000

Nekhoroshev theorem for small amplitude solutions in nonlinear Schrödinger equations

  • D. Bambusi
  • Math. Z
  • 1999

Mather sets for twist maps and geodesics on tori

  • V. Bangert
  • Dynamics Reported
  • 1998

Introduction to Symplectic Topology

  • D. McDuff, D. Salamon
  • Oxford Mathematical Monographs
  • 1995

Variational construction of connecting orbits

  • J. Mather
  • Ann. Inst. Fourier (Grenoble)
  • 1993

Similar Papers

Loading similar papers…