Scaling Rate for Semi-dispersing Billiards with Non-compact Cusps
نویسنده
چکیده
We show that certain billiard tables with non-compact cusps are mixing with respect to the invariant infinite measure, in the sense of Krengel and Sucheston. Moreover, we show that the scaling rate is slower than a certain polynomial rate.
منابع مشابه
Mixing Rate for Semi-dispersing Billiards with Non-compact Cusps
Since the seminal work of Sinai one studies chaotic properties of planar billiards tables. Among them is the study of decay of correlations for these tables. There are examples in the literature of tables with exponential and even polynomial decay. However, until now nothing is known about mixing properties for billiard tables with non-compact cusps. There is no consensual definition of mixing ...
متن کاملConvergence of Moments for Dispersing Billiards with Cusps
Dispersing billiards with cusps are deterministic dynamical systems with a mild degree of chaos, exhibiting “intermittent” behavior that alternates between regular and chaotic patterns. They are characterized by decay of correlations of order 1/n and a central limit theorem with a non-classical scaling factor of √ n logn. As for the growth of the pth moments of the appropriately normalized Birk...
متن کاملLimit Theorems for Dispersing Billiards with Cusps
Dispersing billiards with cusps are deterministic dynamical systems with a mild degree of chaos, exhibiting “intermittent” behavior that alternates between regular and chaotic patterns. Their statistical properties are therefore weak and delicate. They are characterized by a slow (power-law) decay of correlations, and as a result the classical central limit theorem fails. We prove that a non-cl...
متن کاملDispersing billiards with cusps: slow decay of correlations
Dispersing billiards introduced by Sinai are uniformly hyperbolic and have strong statistical properties (exponential decay of correlations and various limit theorems). However, if the billiard table has cusps (corner points with zero interior angles), then its hyperbolicity is nonuniform and statistical properties deteriorate. Until now only heuristic and experiments results existed predicting...
متن کاملDecay of correlations and invariance principles for dispersing billiards with cusps, and related planar billiard flows
Following recent work of Chernov, Markarian, and Zhang, it is known that the billiard map for dispersing billiards with zero angle cusps has slow decay of correlations with rate 1/n. Since the collisions inside a cusp occur in quick succession, it is reasonable to expect a much faster decay rate in continuous time. In this paper we prove that the flow is rapid mixing: correlations decay faster ...
متن کامل