---
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@
...