Paul Jung, Ian Melbourne, Françoise Pène, Paulo Varandas, Hong-Kun Zhang
Published 2019-02-24Version 1
We consider a class of planar dispersing billiards with a cusp at a point of vanishing curvature. Convergence to a stable law and to the corresponding L\'evy process in the $\cM_1$ and $\cM_2$ Skorohod topologies has been studied in recent work. Here we show that certain sufficient conditions for $\cM_2$-convergence are also necessary.
Convergence to $α$-stable Lévy motion for chaotic billiards with several cusps at flat points
Powers of sequences and convergence of ergodic averages
Convergence to a Lévy process in the Skorohod $M_1$ and $M_2$ topologies for nonuniformly hyperbolic systems, including billiards with cusps
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