---
res:
bibo_abstract:
- "The purpose of this paper is to construct examples of diffusion for E-Hamiltonian
perturbations\r\nof completely integrable Hamiltonian systems in 2d-dimensional
phase space, with d large.\r\nIn the first part of the paper, simple and explicit
examples are constructed illustrating absence\r\nof ‘long-time’ stability for
size E Hamiltonian perturbations of quasi-convex integrable systems\r\nalready
when the dimension 2d of phase space becomes as large as log 1/E . We first produce\r\nthe
example in Gevrey class and then a real analytic one, with some additional work.\r\nIn
the second part, we consider again E-Hamiltonian perturbations of completely integrable\r\nHamiltonian
system in 2d-dimensional space with E-small but not too small, |E| > exp(−d),
with\r\nd the number of degrees of freedom assumed large. It is shown that for
a class of analytic\r\ntime-periodic perturbations, there exist linearly diffusing
trajectories. The underlying idea for\r\nboth examples is similar and consists
in coupling a fixed degree of freedom with a large\r\nnumber of them. The procedure
and analytical details are however significantly different. As\r\nmentioned, the
construction in Part I is totally elementary while Part II is more involved, relying\r\nin
particular on the theory of normally hyperbolic invariant manifolds, methods of
generating\r\nfunctions, Aubry–Mather theory, and Mather’s variational methods.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Jean
foaf_name: Bourgain, Jean
foaf_surname: Bourgain
- foaf_Person:
foaf_givenName: Vadim
foaf_name: Kaloshin, Vadim
foaf_surname: Kaloshin
foaf_workInfoHomepage: http://www.librecat.org/personId=FE553552-CDE8-11E9-B324-C0EBE5697425
orcid: 0000-0002-6051-2628
bibo_doi: 10.1016/j.jfa.2004.09.006
bibo_issue: '1'
bibo_volume: 229
dct_date: 2005^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0022-1236
dct_language: eng
dct_publisher: Elsevier@
dct_subject:
- Analysis
dct_title: On diffusion in high-dimensional Hamiltonian systems@
...