A random billiard map in the circle. Issue 2 (3rd April 2022)

• Record Type: Journal Article
• Authors: Vales, Túlio; Pinto-de-Carvalho, Sônia
• Is Part Of: Dynamical systems. Volume 37:Issue 2(2022)
• Page Start: 333
• Page End: 353
• Publication Date: 2022-04-03
• Subjects: Circular billiards -- random billiards -- random maps -- Lyapunov exponents -- Knudsen's law; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2022.2050357
• Languages: English
• ISSNs: 1468-9367

Abstract

Abstract : We consider a random billiard map, the one in which the standard specular reflection rule is replaced by a random reflection given by a Markov operator. We exhibit an invariant measure for random billiards on general tables. In the special case of a circular table we show that almost every (random) orbit is dense in the boundary as well as in the circular ring formed between the circle boundary and the random caustic. We additionally prove Strong Knudsen's Law for a particular case of families of absolutely continuous measures with respect to Liouville. We also calculate the Lyapunov exponent for the random billiard map in the circle.