Improved Estimates for Correlations in Billiards
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We consider several classes of chaotic billiards with slow (polynomial) mixing rates, which include Bunimovich’s stadium and dispersing billiards with cusps. In recent papers by Markarian and the present authors, estimates on the decay of correlations were obtained that were sub-optimal (they contained a redundant logarithmic factor). We sharpen those estimates by removing that factor.
KeywordsUnstable Manifold Conditional Measure Markov Partition Homogeneous Section Consecutive Collision
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