{"publication":"SIAM Review","language":[{"iso":"eng"}],"publication_status":"published","issue":"4","doi":"10.1137/070703235","type":"journal_article","article_type":"original","page":"702-720","_id":"8509","abstract":[{"text":"The goal of this paper is to present to nonspecialists what is perhaps the simplest possible geometrical picture explaining the mechanism of Arnold diffusion. We choose to speak of a specific model—that of geometric rays in a periodic optical medium. This model is equivalent to that of a particle in a periodic potential in ${\\mathbb R}^{n}$ with energy prescribed and to the geodesic flow in a Riemannian metric on ${\\mathbb R}^{n} $.","lang":"eng"}],"volume":50,"date_updated":"2021-01-12T08:19:46Z","oa_version":"None","author":[{"id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim","last_name":"Kaloshin","orcid":"0000-0002-6051-2628","first_name":"Vadim"},{"full_name":"Levi, Mark","first_name":"Mark","last_name":"Levi"}],"status":"public","date_created":"2020-09-18T10:48:12Z","publication_identifier":{"issn":["0036-1445","1095-7200"]},"day":"05","publisher":"Society for Industrial & Applied Mathematics","year":"2008","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"11","date_published":"2008-11-05T00:00:00Z","extern":"1","citation":{"ama":"Kaloshin V, Levi M. Geometry of Arnold diffusion. <i>SIAM Review</i>. 2008;50(4):702-720. doi:<a href=\"https://doi.org/10.1137/070703235\">10.1137/070703235</a>","ieee":"V. Kaloshin and M. Levi, “Geometry of Arnold diffusion,” <i>SIAM Review</i>, vol. 50, no. 4. Society for Industrial &#38; Applied Mathematics, pp. 702–720, 2008.","short":"V. Kaloshin, M. Levi, SIAM Review 50 (2008) 702–720.","mla":"Kaloshin, Vadim, and Mark Levi. “Geometry of Arnold Diffusion.” <i>SIAM Review</i>, vol. 50, no. 4, Society for Industrial &#38; Applied Mathematics, 2008, pp. 702–20, doi:<a href=\"https://doi.org/10.1137/070703235\">10.1137/070703235</a>.","apa":"Kaloshin, V., &#38; Levi, M. (2008). Geometry of Arnold diffusion. <i>SIAM Review</i>. Society for Industrial &#38; Applied Mathematics. <a href=\"https://doi.org/10.1137/070703235\">https://doi.org/10.1137/070703235</a>","ista":"Kaloshin V, Levi M. 2008. Geometry of Arnold diffusion. SIAM Review. 50(4), 702–720.","chicago":"Kaloshin, Vadim, and Mark Levi. “Geometry of Arnold Diffusion.” <i>SIAM Review</i>. Society for Industrial &#38; Applied Mathematics, 2008. <a href=\"https://doi.org/10.1137/070703235\">https://doi.org/10.1137/070703235</a>."},"intvolume":"        50","quality_controlled":"1","title":"Geometry of Arnold diffusion","keyword":["Theoretical Computer Science","Applied Mathematics","Computational Mathematics"]}