{"status":"public","page":"5214-5234","publication":"Nonlinearity","type":"journal_article","extern":"1","publication_identifier":{"issn":["0951-7715","1361-6544"]},"quality_controlled":"1","day":"15","language":[{"iso":"eng"}],"year":"2018","title":"Density of convex billiards with rational caustics","date_created":"2020-09-17T10:42:09Z","abstract":[{"text":"We show that in the space of all convex billiard boundaries, the set of boundaries with rational caustics is dense. More precisely, the set of billiard boundaries with caustics of rotation number 1/q is polynomially sense in the smooth case, and exponentially dense in the analytic case.","lang":"eng"}],"issue":"11","article_processing_charge":"No","publication_status":"published","month":"10","date_updated":"2021-01-12T08:19:10Z","oa":1,"author":[{"last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","first_name":"Vadim"},{"last_name":"Zhang","first_name":"Ke","full_name":"Zhang, Ke"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2018-10-15T00:00:00Z","article_type":"original","publisher":"IOP Publishing","external_id":{"arxiv":["1706.07968"]},"_id":"8420","doi":"10.1088/1361-6544/aadc12","citation":{"ista":"Kaloshin V, Zhang K. 2018. Density of convex billiards with rational caustics. Nonlinearity. 31(11), 5214–5234.","ieee":"V. Kaloshin and K. Zhang, “Density of convex billiards with rational caustics,” <i>Nonlinearity</i>, vol. 31, no. 11. IOP Publishing, pp. 5214–5234, 2018.","ama":"Kaloshin V, Zhang K. Density of convex billiards with rational caustics. <i>Nonlinearity</i>. 2018;31(11):5214-5234. doi:<a href=\"https://doi.org/10.1088/1361-6544/aadc12\">10.1088/1361-6544/aadc12</a>","short":"V. Kaloshin, K. Zhang, Nonlinearity 31 (2018) 5214–5234.","mla":"Kaloshin, Vadim, and Ke Zhang. “Density of Convex Billiards with Rational Caustics.” <i>Nonlinearity</i>, vol. 31, no. 11, IOP Publishing, 2018, pp. 5214–34, doi:<a href=\"https://doi.org/10.1088/1361-6544/aadc12\">10.1088/1361-6544/aadc12</a>.","chicago":"Kaloshin, Vadim, and Ke Zhang. “Density of Convex Billiards with Rational Caustics.” <i>Nonlinearity</i>. IOP Publishing, 2018. <a href=\"https://doi.org/10.1088/1361-6544/aadc12\">https://doi.org/10.1088/1361-6544/aadc12</a>.","apa":"Kaloshin, V., &#38; Zhang, K. (2018). Density of convex billiards with rational caustics. <i>Nonlinearity</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1361-6544/aadc12\">https://doi.org/10.1088/1361-6544/aadc12</a>"},"volume":31,"arxiv":1,"oa_version":"Preprint","keyword":["Mathematical Physics","General Physics and Astronomy","Applied Mathematics","Statistical and Nonlinear Physics"],"main_file_link":[{"url":"https://arxiv.org/abs/1706.07968","open_access":"1"}],"intvolume":"        31"}