2016/05/25 by Zhang, Hong-Kun
#37A25 #37D50 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1605.07714
In this paper we continue to study billiards with flat points, by constructing a spec family of dispersing billiards with cusps. All boundaries of the table have positive curvature except that the curvature vanishes at the vertex of a cusp, i.e. there is a pair of boundaries intersection at the flat point tangentially. We study the mixing rates of this one-parameter family of billiards with parameter β∈ (2,∞), and show that the correlation functions of the collision map decay polynomially with order \cO(n-(1)/(β-1)) as n→∞. In particular, this solves an open question raised by Chernov and Markarian \citeCM05.