@article{8502,
  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.},
  author       = {Kaloshin, Vadim and Saprykina, Maria},
  issn         = {0010-3616},
  journal      = {Communications in Mathematical Physics},
  keywords     = {Mathematical Physics, Statistical and Nonlinear Physics},
  number       = {3},
  pages        = {643--697},
  publisher    = {Springer Nature},
  title        = {{An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension}},
  doi          = {10.1007/s00220-012-1532-x},
  volume       = {315},
  year         = {2012},
}