AI 中文总结
研究二维递归、分段光滑双曲映射分解为K - 混合分量的定理，不设映射保持概率测度，证明满足特定假设的非周期洛伦兹气体是K - 混合的，并讨论其对相关性衰减的影响。
AI 中文摘要
我们证明了一个关于二维递归、分段光滑双曲映射分解为K - 混合分量的一般定理。与经典结果不同，我们不假设该映射保持概率测度。作为应用，我们表明每个满足特定均匀性假设的递归非周期洛伦兹气体是K - 混合的。最后，我们讨论了K - 混合对非周期洛伦兹气体中相对于零均值\(L^1\)可观测量的相关性衰减的一些影响。
英文摘要
We prove a general theorem on the decomposition into K-mixing components for recurrent, piecewise-smooth hyperbolic maps in two dimensions. In contrast with classical results, we do not assume that the map preserves a probability measure. As an application, we show that every recurrent aperiodic Lorentz gas satisfying certain uniformity assumptions is K-mixing. Finally, we discuss some consequences of K-mixing for the decay of correlations relative to zero-mean $L^1$ observables in aperiodic Lorentz gases.
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