--- _id: '8502' abstract: - lang: eng text: '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.' article_processing_charge: No article_type: original author: - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 - first_name: Maria full_name: Saprykina, Maria last_name: Saprykina citation: ama: Kaloshin V, Saprykina M. An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension. Communications in Mathematical Physics. 2012;315(3):643-697. doi:10.1007/s00220-012-1532-x apa: Kaloshin, V., & Saprykina, M. (2012). An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-012-1532-x chicago: Kaloshin, Vadim, and Maria Saprykina. “An Example of a Nearly Integrable Hamiltonian System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension.” Communications in Mathematical Physics. Springer Nature, 2012. https://doi.org/10.1007/s00220-012-1532-x. ieee: V. Kaloshin and M. Saprykina, “An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension,” Communications in Mathematical Physics, vol. 315, no. 3. Springer Nature, pp. 643–697, 2012. ista: Kaloshin V, Saprykina M. 2012. An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension. Communications in Mathematical Physics. 315(3), 643–697. mla: Kaloshin, Vadim, and Maria Saprykina. “An Example of a Nearly Integrable Hamiltonian System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension.” Communications in Mathematical Physics, vol. 315, no. 3, Springer Nature, 2012, pp. 643–97, doi:10.1007/s00220-012-1532-x. short: V. Kaloshin, M. Saprykina, Communications in Mathematical Physics 315 (2012) 643–697. date_created: 2020-09-18T10:47:16Z date_published: 2012-11-01T00:00:00Z date_updated: 2021-01-12T08:19:44Z day: '01' doi: 10.1007/s00220-012-1532-x extern: '1' intvolume: ' 315' issue: '3' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '11' oa_version: None page: 643-697 publication: Communications in Mathematical Physics publication_identifier: issn: - 0010-3616 - 1432-0916 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 315 year: '2012' ...