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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 | Abstract: | In 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 | Services: | Forum | Review | PDF | Favorites |
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