{"extern":"1","year":"2018","keyword":["Mathematical Physics","General Physics and Astronomy","Applied Mathematics","Statistical and Nonlinear Physics"],"citation":{"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>.","ista":"Kaloshin V, Zhang K. 2018. Density of convex billiards with rational caustics. Nonlinearity. 31(11), 5214–5234.","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>","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.","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>.","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."},"quality_controlled":"1","language":[{"iso":"eng"}],"month":"10","publication_status":"published","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1706.07968"}],"publisher":"IOP Publishing","page":"5214-5234","date_created":"2020-09-17T10:42:09Z","title":"Density of convex billiards with rational caustics","volume":31,"article_type":"original","status":"public","external_id":{"arxiv":["1706.07968"]},"publication":"Nonlinearity","_id":"8420","type":"journal_article","day":"15","oa_version":"Preprint","intvolume":"        31","article_processing_charge":"No","oa":1,"author":[{"last_name":"Kaloshin","full_name":"Kaloshin, Vadim","first_name":"Vadim","orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"},{"first_name":"Ke","full_name":"Zhang, Ke","last_name":"Zhang"}],"issue":"11","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"}],"date_published":"2018-10-15T00:00:00Z","publication_identifier":{"issn":["0951-7715","1361-6544"]},"date_updated":"2021-01-12T08:19:10Z","doi":"10.1088/1361-6544/aadc12","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}