In this paper we answer affirmatively the question concerning the existence of hyperbolic billiards in convex domains of ℝ3. We also prove that a related class of semi-focusing billiards has mixed dynamics, i.e., their phase space is an union of two invariant sets of positive measure such that the dynamics is integrable on one set and is hyperbolic on the other. These billiards are the first rigorous examples of billiards in domains of ℝ3 with divided phase space.
Semi-focusing billiards: Hyperbolicity
Del Magno G.
2006-01-01
Abstract
In this paper we answer affirmatively the question concerning the existence of hyperbolic billiards in convex domains of ℝ3. We also prove that a related class of semi-focusing billiards has mixed dynamics, i.e., their phase space is an union of two invariant sets of positive measure such that the dynamics is integrable on one set and is hyperbolic on the other. These billiards are the first rigorous examples of billiards in domains of ℝ3 with divided phase space.File in questo prodotto:
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