{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:38:46Z","timestamp":1753882726223,"version":"3.41.2"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100001807","name":"S\u00e3o Paulo Research Foundation","doi-asserted-by":"crossref","award":["2020\/02415-7","2019\/09150-1","2019\/14038-6"],"award-info":[{"award-number":["2020\/02415-7","2019\/09150-1","2019\/14038-6"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100003593","name":"National Council for Scientific and Technological Development","doi-asserted-by":"crossref","award":["162944\/2020-9","301318\/2019-0"],"award-info":[{"award-number":["162944\/2020-9","301318\/2019-0"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2022,3,30]]},"abstract":"<jats:p> In this paper, we consider the evolution of an ensemble of noninteracting classical particles confined in a closed region. Each one of these particles experiences several elastic collisions with a rigid-smooth oval-like boundary. As known in the literature, numerical simulations for this kind of system demand too much time, mostly because of the time spent in solving transcendental equations. To deal with that, we highlight an alternative approach to speed up the search of solutions for the transcendental equations via the tangent method, which has proved to be a faster way to solve this problem when compared with other methods, like the bisection one. The methods applied here are generic and can be used or adapted for other billiard boundaries. <\/jats:p>","DOI":"10.1142\/s0218127422500523","type":"journal-article","created":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T09:37:34Z","timestamp":1648719454000},"source":"Crossref","is-referenced-by-count":2,"title":["Tangent Method and Some Dynamical Properties of an Oval-Like Billiard"],"prefix":"10.1142","volume":"32","author":[{"given":"Diogo Ricardo","family":"da Costa","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica, Universidade Federal do Paran\u00e1 (UFPR), Curitiba \u2013 CEP 80060-000, PR, Brazil"},{"name":"Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade de S\u00e3o Paulo, S\u00e3o Paulo \u2013 CEP 05508-090, SP, Brazil"},{"name":"Departamento de F\u00edsica, Universidade Estadual Paulista, Rio Claro \u2013 CEP 13506-900, SP, Brazil"}]},{"given":"Matheus","family":"Hansen","sequence":"additional","affiliation":[{"name":"Instituto de Ci\u00eancia e Tecnologia, Universidade Federal de S\u00e3o Paulo, S\u00e3o Jos\u00e9 dos Campos \u2013 CEP 12247-014, SP, Brazil"}]},{"given":"M\u00e1rio Roberto","family":"Silva","sequence":"additional","affiliation":[{"name":"Departamento de Estat\u00edstica, Matem\u00e1tica Aplicada e Computa\u00e7\u00e3o, Universidade Estadual Paulista, Rio Claro \u2013 CEP 13506-900, SP, Brazil"}]},{"given":"Edson D.","family":"Leonel","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidade Estadual Paulista, Rio Claro \u2013 CEP 13506-900, SP, Brazil"}]}],"member":"219","published-online":{"date-parts":[[2022,3,30]]},"reference":[{"key":"S0218127422500523BIB001","doi-asserted-by":"publisher","DOI":"10.1088\/0143-0807\/2\/2\/006"},{"key":"S0218127422500523BIB002","doi-asserted-by":"publisher","DOI":"10.1088\/0953-8984\/11\/38\/201"},{"key":"S0218127422500523BIB003","volume-title":"Dynamical Systems","volume":"9","author":"Birkhoff G. 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