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