[{"quality_controlled":"1","intvolume":" 315","uri_base":"https://research-explorer.app.ist.ac.at","language":[{}],"issue":"3","oa_version":"None","month":"11","status":"public","publication_status":"published","publication_identifier":{"issn":[]},"volume":315,"extern":"1","_id":"8502","author":[{"first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","last_name":"Kaloshin"},{"first_name":"Maria","last_name":"Saprykina"}],"dini_type":"doc-type:article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","keyword":[],"dc":{"source":["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"],"description":["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."],"relation":["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"],"creator":["Kaloshin, Vadim","Saprykina, Maria"],"subject":["Mathematical Physics","Statistical and Nonlinear Physics"],"type":["info:eu-repo/semantics/article","doc-type:article","text","http://purl.org/coar/resource_type/c_6501"],"date":["2012"],"rights":["info:eu-repo/semantics/closedAccess"],"language":["eng"],"title":["An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension"],"identifier":["https://research-explorer.app.ist.ac.at/record/8502"],"publisher":["Springer Nature"]},"publication":"Communications in Mathematical Physics","day":"01","date_updated":"2021-01-12T08:19:44Z","abstract":[{"lang":"eng"}],"date_published":"2012-11-01T00:00:00Z","article_processing_charge":"No","article_type":"original","citation":{"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","short":"V. Kaloshin, M. Saprykina, Communications in Mathematical Physics 315 (2012) 643–697.","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.","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.","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."},"creator":{"login":"dernst","id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},"date_created":"2020-09-18T10:47:16Z","page":"643-697"}]