{"date_created":"2021-05-30T13:58:13Z","oa":1,"_id":"9435","abstract":[{"text":"For any given positive integer l, we prove that every plane deformation of a circlewhich preserves the 1/2and 1/ (2l + 1) -rational caustics is trivial i.e. the deformationconsists only of similarities (rescalings and isometries).","lang":"eng"}],"author":[{"first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","last_name":"Kaloshin"},{"last_name":"Koudjinan","orcid":"0000-0003-2640-4049","full_name":"Koudjinan, Edmond","id":"52DF3E68-AEFA-11EA-95A4-124A3DDC885E","first_name":"Edmond"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"VaKa"}],"file":[{"file_size":353431,"creator":"ekoudjin","file_name":"CoExistence 2&3 caustics 3_17_6_2_3.pdf","content_type":"application/pdf","date_updated":"2021-05-30T13:57:37Z","relation":"main_file","file_id":"9436","date_created":"2021-05-30T13:57:37Z","checksum":"b281b5c2e3e90de0646c3eafcb2c6c25","access_level":"open_access"}],"file_date_updated":"2021-05-30T13:57:37Z","article_processing_charge":"No","language":[{"iso":"eng"}],"title":"Non co-preservation of the 1/2 and  1/(2l+1)-rational caustics along deformations of circles","date_updated":"2021-06-01T09:10:22Z","oa_version":"Submitted Version","has_accepted_license":"1","status":"public","ddc":["500"],"year":"2021","citation":{"short":"V. Kaloshin, E. Koudjinan, (2021).","mla":"Kaloshin, Vadim, and Edmond Koudjinan. <i>Non Co-Preservation of the 1/2 and  1/(2l+1)-Rational Caustics along Deformations of Circles</i>. 2021.","ieee":"V. Kaloshin and E. Koudjinan, “Non co-preservation of the 1/2 and  1/(2l+1)-rational caustics along deformations of circles.” 2021.","chicago":"Kaloshin, Vadim, and Edmond Koudjinan. “Non Co-Preservation of the 1/2 and  1/(2l+1)-Rational Caustics along Deformations of Circles,” 2021.","ista":"Kaloshin V, Koudjinan E. 2021. Non co-preservation of the 1/2 and  1/(2l+1)-rational caustics along deformations of circles.","ama":"Kaloshin V, Koudjinan E. Non co-preservation of the 1/2 and  1/(2l+1)-rational caustics along deformations of circles. 2021.","apa":"Kaloshin, V., &#38; Koudjinan, E. (2021). Non co-preservation of the 1/2 and  1/(2l+1)-rational caustics along deformations of circles."},"date_published":"2021-01-01T00:00:00Z","type":"preprint"}