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