论文标题
精确和K混合动力系统的扩展
Extensions of exact and K-mixing dynamical systems
论文作者
论文摘要
我们考虑了精确的，分别k混合或至少分解为正效应的非单星图的扩展，分别将k混合组件分解为阳性。延伸空间的纤维具有可计数（有限或无限）的基数，对它们的作用假定是溢流性的或生物的。我们将这些系统分别称为纤维 - 释放性和纤维基础扩展。从技术上讲，它们是偏斜的产品，尽管我们在这里采取的观点并不是通常与偏斜产品相关的观点。我们的主要结果是精确的和k混合分解定理。后者可以用来表明大量的周期性洛伦兹气体（在此表示，在此处表示西奈台球的一般组扩展，包括洛伦兹管和板，以任何维度为k混合）。
We consider extensions of non-singular maps which are exact, respectively K-mixing, or at least have a decomposition into positive-measure exact, respectively K-mixing, components. The fibers of the extension spaces have countable (finite or infinite) cardinality and the action on them is assumed surjective or bijective. We call these systems, respectively, fiber-surjective and fiber-bijective extensions. Technically, they are skew products, though the point of view we take here is not the one generally associated with skew products. Our main results are an Exact and a K-mixing Decomposition Theorem. The latter can be used to show that a large number of periodic Lorentz gases (the term denoting here general group extensions of Sinai billiards, including Lorentz tubes and slabs, in any dimension) are K-mixing.
