On the incenters of triangular orbits in elliptic billiard

2013/04/29 by Olga Romaskevich, Romaskevich, Olga
Physics and Astronomy · Mathematics · #Quantum chaos and dynamical systems #Advanced Differential Equations and Dynamical Systems #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1304.7588

Abstract

We consider 3-periodic orbits in an elliptic billiard. Numerical experiments conducted by Dan Reznik have shown that the locus of the centers of inscribed circles of the corresponding triangles is an ellipse. We prove this fact by the complexification of the problem coupled with the complex law or rfelection.

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