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首页> 外文期刊>Transactions of the American Mathematical Society >TOPOLOGICAL CONTACT DYNAMICS II: TOPOLOGICAL AUTOMORPHISMS, CONTACT HOMEOMORPHISMS, AND NON-SMOOTH CONTACT DYNAMICAL SYSTEMS
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TOPOLOGICAL CONTACT DYNAMICS II: TOPOLOGICAL AUTOMORPHISMS, CONTACT HOMEOMORPHISMS, AND NON-SMOOTH CONTACT DYNAMICAL SYSTEMS

机译：拓扑接触动力学II：拓扑自态，接触同态和非光滑接触动力学系统

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摘要

This sequel to our previous paper continues the study of topological contact dynamics and applications to contact dynamics and topological dynamics. We provide further evidence that the topological automorphism groups of a contact structure and a contact form are the appropriate transformation groups of contact dynamical systems. This article includes an examination of the groups of time-one maps of topological contact and strictly contact isotopies, and the construction of a bi-invariant metric on the latter. Moreover, every topological contact or strictly contact dynamical system is arbitrarily close to a continuous contact or strictly contact dynamical system with the same end point. In particular, the above groups of time-one maps are independent of the choice of norm in the definition of the contact distance. On every contact manifold we construct topological contact dynamical systems with time-one maps that fail to be Lipschitz continuous, and smooth contact vector fields whose flows are topologically conjugate but not conjugated by a contact C~1-diffeomorphism.
机译：我们先前论文的续篇继续了拓扑接触动力学的研究及其在接触动力学和拓扑动力学中的应用。我们提供了进一步的证据，表明接触结构和接触形式的拓扑自同构群是接触动力学系统的适当转换群。本文包括对拓扑接触和严格接触同位素的时间一图组的检查，以及在后者上的双不变度量的构造。此外，每个拓扑接触或严格接触动力学系统都任意接近具有相同端点的连续接触或严格接触动力学系统。特别地，上述一组时间一图独立于接触距离的定义中的标准选择。在每个接触流形上，我们构造了具有时间一图的拓扑接触动力学系统，该时间接触图不能是Lipschitz连续的，并且其光滑的接触矢量场的流动在拓扑上是共轭的，但没有被接触C〜1-非同构共轭。

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