Topology of Billiard Problems, I
نویسنده
چکیده
Let T ⊂ R be a strictly convex domain bounded by a smooth hypersurface X = ∂T . In this paper we find lower bounds on the number of billiard trajectories in T , which have a prescribed initial point A ∈ X , a prescribed final point B ∈ X and make a prescribed number n of reflections at the boundary X . We apply a topological approach based on calculation of cohomology rings of certain configurations spaces of Sm.
منابع مشابه
Topology of Billiard Problems, Ii
In this paper we give topological lower bounds on the number of periodic and of closed trajectories in strictly convex smooth billiards T ⊂ Rm+1. Namely, for given n, we estimate the number of n-periodic billiard trajectories in T and also estimate the number of billiard trajectories which start and end at a given point A ∈ ∂T and make a prescribed number n of reflections at the boundary ∂T of ...
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تاریخ انتشار 2002