35 citations · 36 across the 2 of their papers we have counts for
2 papers
math.DS2019★ 1 cited
Necessary and sufficient condition for $\cM_2$-convergence to a Lévy process for billiards with cusps at flat points
Paul Jung, Ian Melbourne, Françoise Pène +2
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 Lévy process in the $\cM_1$ a…
math.DS2013★ 35 cited
Rapid mixing for the Lorenz attractor and statistical limit laws for their time-1 maps
V. Araujo, I. Melbourne, P. Varandas
We prove that every geometric Lorenz attractor has superpolynomial decay of correlations with respect to the unique SRB measure. Moreover, we prove the Central Limit Theorem and Al…