[{"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"}],"keyword":["Theoretical Computer Science","Applied Mathematics","Computational Mathematics"],"extern":"1","quality_controlled":"1","date_published":"2008-11-05T00:00:00Z","author":[{"full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","first_name":"Vadim","orcid":"0000-0002-6051-2628","last_name":"Kaloshin"},{"full_name":"Levi, Mark","last_name":"Levi","first_name":"Mark"}],"doi":"10.1137/070703235","date_updated":"2021-01-12T08:19:46Z","article_processing_charge":"No","oa_version":"None","date_created":"2020-09-18T10:48:12Z","title":"Geometry of Arnold diffusion","publication":"SIAM Review","publisher":"Society for Industrial & Applied Mathematics","citation":{"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.","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>.","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>","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>","ista":"Kaloshin V, Levi M. 2008. Geometry of Arnold diffusion. SIAM Review. 50(4), 702–720.","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>."},"publication_identifier":{"issn":["0036-1445","1095-7200"]},"language":[{"iso":"eng"}],"month":"11","status":"public","article_type":"original","day":"05","issue":"4","intvolume":"        50","_id":"8509","publication_status":"published","year":"2008","page":"702-720","volume":50,"type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}]