Angular Billiard and Algebraic Birkhoff conjecture

2016/01/13 by Michael Bialy, Bialy, Michael, Andrey E. Mironov +1 · 3 citations
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP #nlin.SI

paper · pdf · doi:10.48550/arxiv.1601.03196

20p

arxiv created 2016/01/13 · arxiv updated 2016/01/14

Abstract

In this paper we introduce a new dynamical system which we call Angular billiard. It acts on the exterior points of a convex curve in Euclidean plane. In a neighborhood of the boundary curve this system turns out to be dual to the Birkhoff billiard. Using this system we get new results on algebraic Birkhoff conjecture on integrable billiards.

Cited by

• Integrable Billiards and Related Topics
• On complex algebraic caustics in planar and projective billiards
• Isoperimetric-type inequalities for Mather's β-function of convex billiards

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