An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension Kaloshin, Vadim ; https://orcid.org/0000-0002-6051-2628 Saprykina, Maria Mathematical Physics Statistical and Nonlinear Physics 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. Springer Nature 2012 info:eu-repo/semantics/article doc-type:Article Article http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/8502 Kaloshin V, Saprykina M. An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension. <i>Communications in Mathematical Physics</i>. 2012;315(3):643-697. doi:<a href="https://doi.org/10.1007/s00220-012-1532-x">10.1007/s00220-012-1532-x</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s00220-012-1532-x info:eu-repo/semantics/altIdentifier/issn/0010-3616 info:eu-repo/semantics/altIdentifier/issn/1432-0916 info:eu-repo/semantics/closedAccess