[{"extern":"1","year":"2019","publisher":"Springer Nature","publication_status":"published","author":[{"full_name":"Bálint, Péter","first_name":"Péter","last_name":"Bálint"},{"first_name":"Jacopo","last_name":"De Simoi","full_name":"De Simoi, Jacopo"},{"full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","first_name":"Vadim"},{"full_name":"Leguil, Martin","last_name":"Leguil","first_name":"Martin"}],"volume":374,"date_created":"2020-09-17T10:41:27Z","date_updated":"2021-01-12T08:19:08Z","publication_identifier":{"issn":["0010-3616","1432-0916"]},"month":"05","oa":1,"external_id":{"arxiv":["1809.08947"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1809.08947"}],"quality_controlled":"1","doi":"10.1007/s00220-019-03448-x","language":[{"iso":"eng"}],"type":"journal_article","issue":"3","abstract":[{"lang":"eng","text":"We consider billiards obtained by removing three strictly convex obstacles satisfying the non-eclipse condition on the plane. The restriction of the dynamics to the set of non-escaping orbits is conjugated to a subshift on three symbols that provides a natural labeling of all periodic orbits. We study the following inverse problem: does the Marked Length Spectrum (i.e., the set of lengths of periodic orbits together with their labeling), determine the geometry of the billiard table? We show that from the Marked Length Spectrum it is possible to recover the curvature at periodic points of period two, as well as the Lyapunov exponent of each periodic orbit."}],"_id":"8415","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 374","status":"public","title":"Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards","oa_version":"Preprint","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"article_processing_charge":"No","day":"09","citation":{"ista":"Bálint P, De Simoi J, Kaloshin V, Leguil M. 2019. Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards. Communications in Mathematical Physics. 374(3), 1531–1575.","ieee":"P. Bálint, J. De Simoi, V. Kaloshin, and M. Leguil, “Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards,” Communications in Mathematical Physics, vol. 374, no. 3. Springer Nature, pp. 1531–1575, 2019.","apa":"Bálint, P., De Simoi, J., Kaloshin, V., & Leguil, M. (2019). Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03448-x","ama":"Bálint P, De Simoi J, Kaloshin V, Leguil M. Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards. Communications in Mathematical Physics. 2019;374(3):1531-1575. doi:10.1007/s00220-019-03448-x","chicago":"Bálint, Péter, Jacopo De Simoi, Vadim Kaloshin, and Martin Leguil. “Marked Length Spectrum, Homoclinic Orbits and the Geometry of Open Dispersing Billiards.” Communications in Mathematical Physics. Springer Nature, 2019. https://doi.org/10.1007/s00220-019-03448-x.","mla":"Bálint, Péter, et al. “Marked Length Spectrum, Homoclinic Orbits and the Geometry of Open Dispersing Billiards.” Communications in Mathematical Physics, vol. 374, no. 3, Springer Nature, 2019, pp. 1531–75, doi:10.1007/s00220-019-03448-x.","short":"P. Bálint, J. De Simoi, V. Kaloshin, M. Leguil, Communications in Mathematical Physics 374 (2019) 1531–1575."},"publication":"Communications in Mathematical Physics","page":"1531-1575","article_type":"original","date_published":"2019-05-09T00:00:00Z"},{"article_type":"original","quality_controlled":"1","page":"1173-1228","publication":"Communications in Mathematical Physics","citation":{"ieee":"A. Delshams, V. Kaloshin, A. de la Rosa, and T. M. Seara, “Global instability in the restricted planar elliptic three body problem,” Communications in Mathematical Physics, vol. 366, no. 3. Springer Nature, pp. 1173–1228, 2018.","apa":"Delshams, A., Kaloshin, V., de la Rosa, A., & Seara, T. M. (2018). Global instability in the restricted planar elliptic three body problem. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-018-3248-z","ista":"Delshams A, Kaloshin V, de la Rosa A, Seara TM. 2018. Global instability in the restricted planar elliptic three body problem. Communications in Mathematical Physics. 366(3), 1173–1228.","ama":"Delshams A, Kaloshin V, de la Rosa A, Seara TM. Global instability in the restricted planar elliptic three body problem. Communications in Mathematical Physics. 2018;366(3):1173-1228. doi:10.1007/s00220-018-3248-z","chicago":"Delshams, Amadeu, Vadim Kaloshin, Abraham de la Rosa, and Tere M. Seara. “Global Instability in the Restricted Planar Elliptic Three Body Problem.” Communications in Mathematical Physics. Springer Nature, 2018. https://doi.org/10.1007/s00220-018-3248-z.","short":"A. Delshams, V. Kaloshin, A. de la Rosa, T.M. Seara, Communications in Mathematical Physics 366 (2018) 1173–1228.","mla":"Delshams, Amadeu, et al. “Global Instability in the Restricted Planar Elliptic Three Body Problem.” Communications in Mathematical Physics, vol. 366, no. 3, Springer Nature, 2018, pp. 1173–228, doi:10.1007/s00220-018-3248-z."},"language":[{"iso":"eng"}],"date_published":"2018-09-05T00:00:00Z","doi":"10.1007/s00220-018-3248-z","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"month":"09","day":"05","publication_identifier":{"issn":["0010-3616","1432-0916"]},"article_processing_charge":"No","title":"Global instability in the restricted planar elliptic three body problem","status":"public","publication_status":"published","publisher":"Springer Nature","intvolume":" 366","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"8417","year":"2018","date_updated":"2021-01-12T08:19:08Z","date_created":"2020-09-17T10:41:43Z","volume":366,"oa_version":"None","author":[{"last_name":"Delshams","first_name":"Amadeu","full_name":"Delshams, Amadeu"},{"orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","first_name":"Vadim","full_name":"Kaloshin, Vadim"},{"full_name":"de la Rosa, Abraham","last_name":"de la Rosa","first_name":"Abraham"},{"full_name":"Seara, Tere M.","last_name":"Seara","first_name":"Tere M."}],"type":"journal_article","extern":"1","abstract":[{"text":"The restricted planar elliptic three body problem (RPETBP) describes the motion of a massless particle (a comet or an asteroid) under the gravitational field of two massive bodies (the primaries, say the Sun and Jupiter) revolving around their center of mass on elliptic orbits with some positive eccentricity. The aim of this paper is to show the existence of orbits whose angular momentum performs arbitrary excursions in a large region. In particular, there exist diffusive orbits, that is, with a large variation of angular momentum. The leading idea of the proof consists in analyzing parabolic motions of the comet. By a well-known result of McGehee, the union of future (resp. past) parabolic orbits is an analytic manifold P+ (resp. P−). In a properly chosen coordinate system these manifolds are stable (resp. unstable) manifolds of a manifold at infinity P∞, which we call the manifold at parabolic infinity. On P∞ it is possible to define two scattering maps, which contain the map structure of the homoclinic trajectories to it, i.e. orbits parabolic both in the future and the past. Since the inner dynamics inside P∞ is trivial, two different scattering maps are used. The combination of these two scattering maps permits the design of the desired diffusive pseudo-orbits. Using shadowing techniques and these pseudo orbits we show the existence of true trajectories of the RPETBP whose angular momentum varies in any predetermined fashion.","lang":"eng"}],"issue":"3"},{"type":"journal_article","extern":"1","abstract":[{"text":"In this paper we study a so-called separatrix map introduced by Zaslavskii–Filonenko (Sov Phys JETP 27:851–857, 1968) and studied by Treschev (Physica D 116(1–2):21–43, 1998; J Nonlinear Sci 12(1):27–58, 2002), Piftankin (Nonlinearity (19):2617–2644, 2006) Piftankin and Treshchëv (Uspekhi Mat Nauk 62(2(374)):3–108, 2007). We derive a second order expansion of this map for trigonometric perturbations. In Castejon et al. (Random iteration of maps of a cylinder and diffusive behavior. Preprint available at arXiv:1501.03319, 2015), Guardia and Kaloshin (Stochastic diffusive behavior through big gaps in a priori unstable systems (in preparation), 2015), and Kaloshin et al. (Normally Hyperbolic Invariant Laminations and diffusive behavior for the generalized Arnold example away from resonances. Preprint available at http://www.terpconnect.umd.edu/vkaloshi/, 2015), applying the results of the present paper, we describe a class of nearly integrable deterministic systems with stochastic diffusive behavior.","lang":"eng"}],"publisher":"Springer Nature","intvolume":" 348","publication_status":"published","title":"A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems","status":"public","_id":"8493","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2016","volume":348,"oa_version":"None","date_created":"2020-09-18T10:45:50Z","date_updated":"2021-01-12T08:19:39Z","author":[{"last_name":"Guardia","first_name":"M.","full_name":"Guardia, M."},{"last_name":"Kaloshin","first_name":"Vadim","orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim"},{"full_name":"Zhang, J.","first_name":"J.","last_name":"Zhang"}],"article_processing_charge":"No","publication_identifier":{"issn":["0010-3616","1432-0916"]},"month":"11","day":"01","page":"321-361","article_type":"original","quality_controlled":"1","citation":{"chicago":"Guardia, M., Vadim Kaloshin, and J. Zhang. “A Second Order Expansion of the Separatrix Map for Trigonometric Perturbations of a Priori Unstable Systems.” Communications in Mathematical Physics. Springer Nature, 2016. https://doi.org/10.1007/s00220-016-2705-9.","mla":"Guardia, M., et al. “A Second Order Expansion of the Separatrix Map for Trigonometric Perturbations of a Priori Unstable Systems.” Communications in Mathematical Physics, vol. 348, Springer Nature, 2016, pp. 321–61, doi:10.1007/s00220-016-2705-9.","short":"M. Guardia, V. Kaloshin, J. Zhang, Communications in Mathematical Physics 348 (2016) 321–361.","ista":"Guardia M, Kaloshin V, Zhang J. 2016. A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems. Communications in Mathematical Physics. 348, 321–361.","ieee":"M. Guardia, V. Kaloshin, and J. Zhang, “A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems,” Communications in Mathematical Physics, vol. 348. Springer Nature, pp. 321–361, 2016.","apa":"Guardia, M., Kaloshin, V., & Zhang, J. (2016). A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-016-2705-9","ama":"Guardia M, Kaloshin V, Zhang J. A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems. Communications in Mathematical Physics. 2016;348:321-361. doi:10.1007/s00220-016-2705-9"},"publication":"Communications in Mathematical Physics","language":[{"iso":"eng"}],"doi":"10.1007/s00220-016-2705-9","date_published":"2016-11-01T00:00:00Z"},{"date_published":"2012-11-01T00:00:00Z","doi":"10.1007/s00220-012-1532-x","language":[{"iso":"eng"}],"publication":"Communications in Mathematical Physics","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.","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.","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","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.","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"},"article_type":"original","quality_controlled":"1","page":"643-697","month":"11","day":"01","article_processing_charge":"No","publication_identifier":{"issn":["0010-3616","1432-0916"]},"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"author":[{"id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","first_name":"Vadim","last_name":"Kaloshin","full_name":"Kaloshin, Vadim"},{"full_name":"Saprykina, Maria","first_name":"Maria","last_name":"Saprykina"}],"date_created":"2020-09-18T10:47:16Z","date_updated":"2021-01-12T08:19:44Z","oa_version":"None","volume":315,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"8502","year":"2012","title":"An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension","status":"public","publication_status":"published","publisher":"Springer Nature","intvolume":" 315","abstract":[{"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.","lang":"eng"}],"issue":"3","extern":"1","type":"journal_article"},{"intvolume":" 211","publisher":"Springer Nature","publication_status":"published","status":"public","title":"Generic diffeomorphisms with superexponential growth of number of periodic orbits","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"8525","year":"2000","oa_version":"None","volume":211,"date_created":"2020-09-18T10:50:20Z","date_updated":"2021-01-12T08:19:52Z","author":[{"full_name":"Kaloshin, Vadim","first_name":"Vadim","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628"}],"type":"journal_article","extern":"1","abstract":[{"text":"Let M be a smooth compact manifold of dimension at least 2 and Diffr(M) be the space of C r smooth diffeomorphisms of M. Associate to each diffeomorphism f;isin; Diffr(M) the sequence P n (f) of the number of isolated periodic points for f of period n. In this paper we exhibit an open set N in the space of diffeomorphisms Diffr(M) such for a Baire generic diffeomorphism f∈N the number of periodic points P n f grows with a period n faster than any following sequence of numbers {a n } n ∈ Z + along a subsequence, i.e. P n (f)>a ni for some n i →∞ with i→∞. In the cases of surface diffeomorphisms, i.e. dim M≡2, an open set N with a supergrowth of the number of periodic points is a Newhouse domain. A proof of the man result is based on the Gontchenko–Shilnikov–Turaev Theorem [GST]. A complete proof of that theorem is also presented.","lang":"eng"}],"page":"253-271","quality_controlled":"1","article_type":"original","citation":{"chicago":"Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits.” Communications in Mathematical Physics. Springer Nature, 2000. https://doi.org/10.1007/s002200050811.","short":"V. Kaloshin, Communications in Mathematical Physics 211 (2000) 253–271.","mla":"Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits.” Communications in Mathematical Physics, vol. 211, Springer Nature, 2000, pp. 253–71, doi:10.1007/s002200050811.","apa":"Kaloshin, V. (2000). Generic diffeomorphisms with superexponential growth of number of periodic orbits. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s002200050811","ieee":"V. Kaloshin, “Generic diffeomorphisms with superexponential growth of number of periodic orbits,” Communications in Mathematical Physics, vol. 211. Springer Nature, pp. 253–271, 2000.","ista":"Kaloshin V. 2000. Generic diffeomorphisms with superexponential growth of number of periodic orbits. Communications in Mathematical Physics. 211, 253–271.","ama":"Kaloshin V. Generic diffeomorphisms with superexponential growth of number of periodic orbits. Communications in Mathematical Physics. 2000;211:253-271. doi:10.1007/s002200050811"},"publication":"Communications in Mathematical Physics","language":[{"iso":"eng"}],"doi":"10.1007/s002200050811","date_published":"2000-04-01T00:00:00Z","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"article_processing_charge":"No","publication_identifier":{"issn":["0010-3616","1432-0916"]},"day":"01","month":"04"}]