منابع مشابه
On Conjugacy of Convex Billiards
Given a strictly convex domain Ω ⊂ R2, there is a natural way to define a billiard map in it: a rectilinear path hitting the boundary reflects so that the angle of reflection is equal to the angle of incidence. In this paper we answer a relatively old question of Guillemin. We show that if two billiard maps are C2-conjugate near the boundary, then the corresponding domains are similar, i.e. the...
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The main result of this paper is, that for convex billiards in higher dimensions, in contrast with 2D case, for every point on the boundary and for every n there always exist billiard trajectories developing conjugate points at the n-th collision with the boundary. We shall explain that this is a consequence of the following variational property of the billiard orbits in higher dimension. If a ...
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We give a lower bound on the number of periodic billiard trajectories inside a generic smooth strictly convex closed surface in 3-space: for odd n, there are at least 2(n − 1) such trajectories. Convex plane billiards were studied by G. Birkhoff, and the case of higher dimensional billiards is considered in our previous papers. We apply a topological approach based on the calculation of cohomol...
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 2017
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2016.07.001