Angular billiard and algebraic Birkhoff conjecture

Misha Bialy; Andrey E. Mironov

doi:10.1016/j.aim.2017.04.001

Angular billiard and algebraic Birkhoff conjecture

Misha Bialy^*
, Andrey E. Mironov

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

39 Scopus citations

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.

Original language	English
Pages (from-to)	102-126
Number of pages	25
Journal	Advances in Mathematics
Volume	313
DOIs	https://doi.org/10.1016/j.aim.2017.04.001
State	Published - 20 Jun 2017

Keywords

Birkhoff billiards
Birkhoff conjecture
Polynomial integrals

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10.1016/j.aim.2017.04.001

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title = "Angular billiard and algebraic Birkhoff conjecture",

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.",

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AU - Mironov, Andrey E.

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AB - 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.

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KW - Birkhoff conjecture

KW - Polynomial integrals

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Angular billiard and algebraic Birkhoff conjecture

Abstract

Keywords

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