{"publisher":"Springer","abstract":[{"lang":"eng","text":"In this paper we investigate the existence of closed billiard trajectories in not necessarily smooth convex bodies. In particular, we show that if a body K ⊂ Rd has the property that the tangent cone of every non-smooth point q ∉ ∂K is acute (in a certain sense), then there is a closed billiard trajectory in K."}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa":1,"oa_version":"Preprint","page":"833 - 845","ec_funded":1,"doi":"10.1007/s11856-016-1429-z","publication":"Israel Journal of Mathematics","year":"2016","language":[{"iso":"eng"}],"day":"15","date_updated":"2021-01-12T06:49:56Z","publist_id":"5938","intvolume":"       216","main_file_link":[{"url":"https://arxiv.org/abs/1506.06014","open_access":"1"}],"citation":{"short":"A. Akopyan, A. Balitskiy, Israel Journal of Mathematics 216 (2016) 833–845.","chicago":"Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute Angles.” <i>Israel Journal of Mathematics</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s11856-016-1429-z\">https://doi.org/10.1007/s11856-016-1429-z</a>.","ama":"Akopyan A, Balitskiy A. Billiards in convex bodies with acute angles. <i>Israel Journal of Mathematics</i>. 2016;216(2):833-845. doi:<a href=\"https://doi.org/10.1007/s11856-016-1429-z\">10.1007/s11856-016-1429-z</a>","ieee":"A. Akopyan and A. Balitskiy, “Billiards in convex bodies with acute angles,” <i>Israel Journal of Mathematics</i>, vol. 216, no. 2. Springer, pp. 833–845, 2016.","ista":"Akopyan A, Balitskiy A. 2016. Billiards in convex bodies with acute angles. Israel Journal of Mathematics. 216(2), 833–845.","apa":"Akopyan, A., &#38; Balitskiy, A. (2016). Billiards in convex bodies with acute angles. <i>Israel Journal of Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s11856-016-1429-z\">https://doi.org/10.1007/s11856-016-1429-z</a>","mla":"Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute Angles.” <i>Israel Journal of Mathematics</i>, vol. 216, no. 2, Springer, 2016, pp. 833–45, doi:<a href=\"https://doi.org/10.1007/s11856-016-1429-z\">10.1007/s11856-016-1429-z</a>."},"month":"10","author":[{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"first_name":"Alexey","last_name":"Balitskiy","full_name":"Balitskiy, Alexey"}],"date_published":"2016-10-15T00:00:00Z","title":"Billiards in convex bodies with acute angles","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734"}],"scopus_import":1,"date_created":"2018-12-11T11:51:24Z","acknowledgement":"Supported by People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n°[291734]. Supported by the Russian Foundation for Basic Research grant 15-31-20403 (mol a ved), by the Russian Foundation for Basic Research grant 15-01-99563 A, in part by the Moebius Contest Foundation for Young Scientists, and in part by the Simons Foundation.","issue":"2","department":[{"_id":"HeEd"}],"type":"journal_article","_id":"1330","status":"public","publication_status":"published","quality_controlled":"1","volume":216}