[{"language":[{"iso":"eng"}],"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."}],"publication_identifier":{"issn":["0010-3616","1432-0916"]},"volume":315,"date_published":"2012-11-01T00:00:00Z","page":"643-697","status":"public","article_processing_charge":"No","date_updated":"2021-01-12T08:19:44Z","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"3","type":"journal_article","citation":{"short":"V. Kaloshin, M. Saprykina, Communications in Mathematical Physics 315 (2012) 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.","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.","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","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.","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","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."},"publication_status":"published","author":[{"orcid":"0000-0002-6051-2628","first_name":"Vadim","last_name":"Kaloshin","full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"},{"first_name":"Maria","last_name":"Saprykina","full_name":"Saprykina, Maria"}],"article_type":"original","_id":"8502","oa_version":"None","year":"2012","date_created":"2020-09-18T10:47:16Z","month":"11","title":"An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"intvolume":" 315","doi":"10.1007/s00220-012-1532-x","extern":"1","quality_controlled":"1","day":"01","publication":"Communications in Mathematical Physics"}]