{"title":"Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders","oa_version":"None","page":"1-79","date_published":"2016-09-28T00:00:00Z","date_created":"2020-09-18T10:46:07Z","publisher":"Institut Mittag-Leffler","abstract":[{"text":"We prove a form of Arnold diffusion in the a-priori stable case. Let\r\nH0(p)+ϵH1(θ,p,t),θ∈Tn,p∈Bn,t∈T=R/T,\r\nbe a nearly integrable system of arbitrary degrees of freedom n⩾2 with a strictly convex H0. We show that for a “generic” ϵH1, there exists an orbit (θ,p) satisfying\r\n∥p(t)−p(0)∥>l(H1)>0,\r\nwhere l(H1) is independent of ϵ. The diffusion orbit travels along a codimension-1 resonance, and the only obstruction to our construction is a finite set of additional resonances.\r\n\r\nFor the proof we use a combination of geometric and variational methods, and manage to adapt tools which have recently been developed in the a-priori unstable case.","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"09","author":[{"full_name":"Bernard, Patrick","first_name":"Patrick","last_name":"Bernard"},{"full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","first_name":"Vadim","orcid":"0000-0002-6051-2628"},{"full_name":"Zhang, Ke","first_name":"Ke","last_name":"Zhang"}],"citation":{"short":"P. Bernard, V. Kaloshin, K. Zhang, Acta Mathematica 217 (2016) 1–79.","apa":"Bernard, P., Kaloshin, V., &#38; Zhang, K. (2016). Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders. <i>Acta Mathematica</i>. Institut Mittag-Leffler. <a href=\"https://doi.org/10.1007/s11511-016-0141-5\">https://doi.org/10.1007/s11511-016-0141-5</a>","mla":"Bernard, Patrick, et al. “Arnold Diffusion in Arbitrary Degrees of Freedom and Normally Hyperbolic Invariant Cylinders.” <i>Acta Mathematica</i>, vol. 217, no. 1, Institut Mittag-Leffler, 2016, pp. 1–79, doi:<a href=\"https://doi.org/10.1007/s11511-016-0141-5\">10.1007/s11511-016-0141-5</a>.","ieee":"P. Bernard, V. Kaloshin, and K. Zhang, “Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders,” <i>Acta Mathematica</i>, vol. 217, no. 1. Institut Mittag-Leffler, pp. 1–79, 2016.","ista":"Bernard P, Kaloshin V, Zhang K. 2016. Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders. Acta Mathematica. 217(1), 1–79.","ama":"Bernard P, Kaloshin V, Zhang K. Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders. <i>Acta Mathematica</i>. 2016;217(1):1-79. doi:<a href=\"https://doi.org/10.1007/s11511-016-0141-5\">10.1007/s11511-016-0141-5</a>","chicago":"Bernard, Patrick, Vadim Kaloshin, and Ke Zhang. “Arnold Diffusion in Arbitrary Degrees of Freedom and Normally Hyperbolic Invariant Cylinders.” <i>Acta Mathematica</i>. Institut Mittag-Leffler, 2016. <a href=\"https://doi.org/10.1007/s11511-016-0141-5\">https://doi.org/10.1007/s11511-016-0141-5</a>."},"status":"public","date_updated":"2021-01-12T08:19:39Z","day":"28","extern":"1","year":"2016","_id":"8494","language":[{"iso":"eng"}],"publication_status":"published","quality_controlled":"1","volume":217,"publication_identifier":{"issn":["0001-5962"]},"article_type":"original","intvolume":"       217","issue":"1","type":"journal_article","doi":"10.1007/s11511-016-0141-5","publication":"Acta Mathematica","article_processing_charge":"No"}