Scholarlink

<p>We describe some dynamical properties of one parameter families of billiards on convex curves (ovals) which are deformed by the curvature (curve-shortening) flow. We obtain the bifurcations of the period two orbits and some special non-Birkhoff orbits, the normal periodic orbits. We prove the destruction of non-convex caustics of the ellipse by deforming it through the curvature flow. This work has some results from the doctoral thesis Damasceno (Família de aplicações bilhares geradas pelo fluxo de curvature. Tese de Doutorado, UNICAMP, 2011) and Salazar (Região de Instabilidade em Bilhares. tese de Doutorado, UFMG, 2019).</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Bifurcations in the Family of Billiards Associated with the Curvature Flow

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月9日

查看全文
  • J. G. Damasceno,
  • M. J. Dias Carneiro,
  • C. M. Salazar

摘要

We describe some dynamical properties of one parameter families of billiards on convex curves (ovals) which are deformed by the curvature (curve-shortening) flow. We obtain the bifurcations of the period two orbits and some special non-Birkhoff orbits, the normal periodic orbits. We prove the destruction of non-convex caustics of the ellipse by deforming it through the curvature flow. This work has some results from the doctoral thesis Damasceno (Família de aplicações bilhares geradas pelo fluxo de curvature. Tese de Doutorado, UNICAMP, 2011) and Salazar (Região de Instabilidade em Bilhares. tese de Doutorado, UFMG, 2019).