Abstract

Dynamic systems acting on the plane and possessing the Wada property have been observed. There exist only two topological types, symmetric and antisymmetric, of dissipative dynamic systems with the nonwandering continuum being a common boundary of three regions. An antisymmetric dynamic system with the nonwandering continuum can be transformed into a dynamic system with an invariant vortex street without fixed points. A further factorization procedure allows obtaining a dynamic system having the Wada property with the nonwandering continuum being a common boundary of any finite number of regions. Moreover, following this strategy, it is possible to construct a Birkhoff curve that is a common boundary of two regions (problem \(1100\) ).

中文翻译：

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拥有和田财产的非流浪连续体

摘要

已经观察到作用在平面上并具有 Wada 特性的动态系统。仅存在对称和反对称两种拓扑类型的耗散动态系统，其中非漂移连续体是三个区域的公共边界。具有非游移连续统的反对称动态系统可以转化为具有不变涡街的无不动点的动态系统。进一步的分解过程允许获得具有 Wada 属性的动态系统，其中非游移连续体是任何有限数量区域的公共边界。此外，按照这个策略，可以构建一个 Birkhoff 曲线，它是两个区域的公共边界（问题\(1100\)）。