Poisson Approximations and Convergence Rates for Hyperbolic Dynamical Systems

Abstract

We prove the asymptotic functional Poisson laws in the total variation norm and obtain estimates of the corresponding convergence rates for a large class of hyperbolic dynamical systems. These results generalize the ones obtained before in this area. Applications to intermittent solenoids, Axiom A systems, Hénon attractors and to billiards, are also considered.

arXiv commentWe are indebted to Ian Melbourne for his useful comments. Few types in Chapter 3 are corrected, the main results unchanged

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• High-Power Directional Emission from Microlasers with Chaotic Resonators
• Ray and wave chaos in asymmetric resonant optical cavities
• Almost Sure Invariance Principle For Nonuniformly Hyperbolic Systems
• Billiards with polynomial mixing rates
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