---
res:
bibo_abstract:
- 'The famous ergodic hypothesis suggests that for a typical Hamiltonian on a typical
energy surface nearly all trajectories are dense. KAM theory disproves it. Ehrenfest
(The Conceptual Foundations of the Statistical Approach in Mechanics. Ithaca,
NY: Cornell University Press, 1959) and Birkhoff (Collected Math Papers. Vol 2,
New York: Dover, pp 462–465, 1968) stated the quasi-ergodic hypothesis claiming
that a typical Hamiltonian on a typical energy surface has a dense orbit. This
question is wide open. Herman (Proceedings of the International Congress of Mathematicians,
Vol II (Berlin, 1998). Doc Math 1998, Extra Vol II, Berlin: Int Math Union, pp
797–808, 1998) proposed to look for an example of a Hamiltonian near H0(I)=⟨I,I⟩2
with a dense orbit on the unit energy surface. In this paper we construct a Hamiltonian
H0(I)+εH1(θ,I,ε) which has an orbit dense in a set of maximal Hausdorff dimension
equal to 5 on the unit energy surface.@eng'
bibo_authorlist:
- 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
- foaf_Person:
foaf_givenName: Maria
foaf_name: Saprykina, Maria
foaf_surname: Saprykina
bibo_doi: 10.1007/s00220-012-1532-x
bibo_issue: '3'
bibo_volume: 315
dct_date: 2012^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0010-3616
- http://id.crossref.org/issn/1432-0916
dct_language: eng
dct_publisher: Springer Nature@
dct_subject:
- Mathematical Physics
- Statistical and Nonlinear Physics
dct_title: An example of a nearly integrable Hamiltonian system with a trajectory
dense in a set of maximal Hausdorff dimension@
...