Semi-dispersing billiards with an infinite cusp
نویسنده
چکیده
Let f : [0,+∞) −→ (0,+∞) be a sufficiently smooth convex function, vanishing at infinity. Consider the planar domain Q delimited by the positive x-semiaxis, the positive y-semiaxis, and the graph of f . Under certain conditions on f , we prove that the billiard flow in Q has a hyperbolic structure and, for some examples, that it is also ergodic. This is done using the cross section corresponding to collisions with the dispersing part of the boundary. The relevant invariant measure for this Poincaré section is infinite, whence the need to surpass the existing results, designed for finitemeasure dynamical systems.
منابع مشابه
Semi - dispersing billiards with an infinite cusp Marco Lenci
Let f : [0,+∞) → (0,+∞) be a sufficiently smooth convex function, vanishing at infinity. Consider the planar domain Q delimited by the positive x-semiaxis, the positive y-semiaxis, and the graph of f . Under certain conditions on f , we prove that the billiard flow in Q has a hyperbolic structure and, with some extra requirements, that it is also ergodic. This is done using the cross section co...
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Let f : [0,+∞) −→ (0,+∞) be a sufficiently smooth convex function, vanishing at infinity. Consider the planar domain Q delimited by the positive x-semiaxis, the positive y-semiaxis, and the graph of f . Under certain conditions on f , we prove that the billiard flow in Q has a hyperbolic structure and, for some examples, that it is also ergodic. This is done using the cross section correspondin...
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تاریخ انتشار 2008