2011/12/11 by Nicolas Bédaride, Nicolas Bedaride, Bedaride, Nicolas +3
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS
paper · pdf · doi:10.48550/arxiv.1112.2370
To appear Proceedings of the American Mathematical Society
openalex publication_date 2011/12/11 · arxiv created 2012/10/21 · arxiv updated 2014/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A simplex is the convex hull of n+1 points in ℝn which form an affine basis. A regular simplex Δn is a simplex with sides of the same length. We consider the billiard flow inside a regular simplex of ℝn. We show the existence of two types of periodic trajectories. One has period n+1 and hits once each face. The other one has period 2n and hits n times one of the faces while hitting once any other face. In both cases we determine the exact coordinates for the points where the trajectory hits the boundary of the simplex.