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- W2891389704 abstract "We consider billiards with several possibly non-isometric and asymmetric cusps at flat points; the case of a single symmetric cusp was studied previously in Zhang (2017) and Jung & Zhang (2018). In particular, we show that properly normalized Birkhoff sums of Holder observables, with respect to the billiard map, converge in Skorokhod's $M_1$-topology to an $alpha$-stable Levy motion, where $alpha$ depends on the `curvature' of the flattest points and the skewness parameter $xi$ depends on the values of the observable at those same points. Previously, Jung & Zhang (2018) proved convergence of the one-point marginals to totally skewed $alpha$-stable distributions for a single symmetric cusp. The limits we prove here are stronger, since they are in the functional sense, but also allow for more varied behaviour due to the presence of multiple cusps. In particular, the general limits we obtain allow for any skewness parameter, as opposed to just the totally skewed cases. We also show that convergence in the stronger $J_1$-topology is not possible." @default.
- W2891389704 created "2018-09-27" @default.
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- W2891389704 date "2018-09-21" @default.
- W2891389704 modified "2023-09-27" @default.
- W2891389704 title "Convergence to $alpha$-stable L'evy motion for chaotic billiards with several cusps at flat points" @default.
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