{"publication_status":"published","extern":"1","title":"Arnold diffusion for smooth convex systems of two and a half degrees of freedom","status":"public","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_type":"original","date_created":"2020-09-18T10:46:43Z","language":[{"iso":"eng"}],"oa_version":"None","keyword":["Mathematical Physics","General Physics and Astronomy","Applied Mathematics","Statistical and Nonlinear Physics"],"date_published":"2015-06-30T00:00:00Z","month":"06","year":"2015","publisher":"IOP Publishing","volume":28,"type":"journal_article","day":"30","publication_identifier":{"issn":["0951-7715","1361-6544"]},"_id":"8498","publication":"Nonlinearity","abstract":[{"text":"In the present note we announce a proof of a strong form of Arnold diffusion for smooth convex Hamiltonian systems. Let ${\\mathbb T}^2$  be a 2-dimensional torus and B2 be the unit ball around the origin in ${\\mathbb R}^2$ . Fix ρ > 0. Our main result says that for a 'generic' time-periodic perturbation of an integrable system of two degrees of freedom $H_0(p)+\\varepsilon H_1(\\theta,p,t),\\quad \\ \\theta\\in {\\mathbb T}^2,\\ p\\in B^2,\\ t\\in {\\mathbb T}={\\mathbb R}/{\\mathbb Z}$ , with a strictly convex H0, there exists a ρ-dense orbit (θε, pε, t)(t) in ${\\mathbb T}^2 \\times B^2 \\times {\\mathbb T}$ , namely, a ρ-neighborhood of the orbit contains ${\\mathbb T}^2 \\times B^2 \\times {\\mathbb T}$ .\r\n\r\nOur proof is a combination of geometric and variational methods. The fundamental elements of the construction are the usage of crumpled normally hyperbolic invariant cylinders from [9], flower and simple normally hyperbolic invariant manifolds from [36] as well as their kissing property at a strong double resonance. This allows us to build a 'connected' net of three-dimensional normally hyperbolic invariant manifolds. To construct diffusing orbits along this net we employ a version of the Mather variational method [41] equipped with weak KAM theory [28], proposed by Bernard in [7].","lang":"eng"}],"date_updated":"2021-01-12T08:19:41Z","quality_controlled":"1","page":"2699-2720","author":[{"first_name":"Vadim","orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim","last_name":"Kaloshin"},{"last_name":"Zhang","full_name":"Zhang, K","first_name":"K"}],"citation":{"chicago":"Kaloshin, Vadim, and K Zhang. “Arnold Diffusion for Smooth Convex Systems of Two and a Half Degrees of Freedom.” <i>Nonlinearity</i>. IOP Publishing, 2015. <a href=\"https://doi.org/10.1088/0951-7715/28/8/2699\">https://doi.org/10.1088/0951-7715/28/8/2699</a>.","mla":"Kaloshin, Vadim, and K. Zhang. “Arnold Diffusion for Smooth Convex Systems of Two and a Half Degrees of Freedom.” <i>Nonlinearity</i>, vol. 28, no. 8, IOP Publishing, 2015, pp. 2699–720, doi:<a href=\"https://doi.org/10.1088/0951-7715/28/8/2699\">10.1088/0951-7715/28/8/2699</a>.","apa":"Kaloshin, V., &#38; Zhang, K. (2015). Arnold diffusion for smooth convex systems of two and a half degrees of freedom. <i>Nonlinearity</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/0951-7715/28/8/2699\">https://doi.org/10.1088/0951-7715/28/8/2699</a>","ieee":"V. Kaloshin and K. Zhang, “Arnold diffusion for smooth convex systems of two and a half degrees of freedom,” <i>Nonlinearity</i>, vol. 28, no. 8. IOP Publishing, pp. 2699–2720, 2015.","ista":"Kaloshin V, Zhang K. 2015. Arnold diffusion for smooth convex systems of two and a half degrees of freedom. Nonlinearity. 28(8), 2699–2720.","ama":"Kaloshin V, Zhang K. Arnold diffusion for smooth convex systems of two and a half degrees of freedom. <i>Nonlinearity</i>. 2015;28(8):2699-2720. doi:<a href=\"https://doi.org/10.1088/0951-7715/28/8/2699\">10.1088/0951-7715/28/8/2699</a>","short":"V. Kaloshin, K. Zhang, Nonlinearity 28 (2015) 2699–2720."},"intvolume":"        28","issue":"8","doi":"10.1088/0951-7715/28/8/2699"}