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28 March 2024
 
  » arxiv » nlin.CD/0201052

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More ergodic billiards with an infinite cusp
Marco Lenci ;
Date 27 Dec 2001
Journal Chaos 13 (2003), no. 1, 105-111 DOI: 10.1063/1.1539802
Subject Chaotic Dynamics; Dynamical Systems | nlin.CD math.DS
AbstractIn a previous paper (nlin.CD/0107041) the following class of billiards was studied: For $f: [0, +infty) longrightarrow (0, +infty)$ convex, sufficiently smooth, and vanishing at infinity, let the billiard table be defined by $Q$, the planar domain delimited by the positive $x$-semiaxis, the positive $y$-semiaxis, and the graph of $f$. For a large class of $f$ we proved that the billiard map was hyperbolic. Furthermore we gave an example of a family of $f$ that makes this map ergodic. Here we extend the latter result to a much wider class of functions.
Source arXiv, nlin.CD/0201052
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