Hyperbolicity of asymmetric lemon billiards*XJ is supported in part by the NSF Grant DMS-1854232. (10th November 2020)

• Record Type: Journal Article
• Authors: Jin, Xin; Zhang, Pengfei
• Is Part Of: Nonlinearity. Volume 34:Number 1(2021)
• Page Start: 92
• Page End: 117
• Publication Date: 2020-11-10
• Subjects: asymmetric lemon -- hyperbolic -- chaotic billiards -- invariant cone field; 37D50; XXXX; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/abaff2
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: Asymmetric lemon billiards was introduced in Chen et al (2013 Chaos 23 043137), where the billiard table Q ( r, b, R ) is the intersection of two round disks with radii r ⩽ R, respectively, and b measures the distance between the two centres. It is conjectured Bunimovich et al (2016 Commun. Math. Phys. 341 781–803) that the asymmetric lemon billiards is hyperbolic when the arc Γ r is a major arc and R is large. In this paper we prove this conjecture for sufficiently large R .