论文标题
通过可数结构对一维动力系统的分类
Classification of one dimensional dynamical systems by countable structures
论文作者
论文摘要
我们研究了在某些紧凑的迁移空间上在动态系统上共轭问题的分类问题的复杂性。尤其是我们证明，间隔动力学系统的共轭等效关系是可计数图的同构等效关系的Borel。这解决了Hjorth的猜想的特殊情况，该猜想指出，封闭单位间隔的所有同件同态群体的连续作用所引起的每个轨道等效关系都可以通过可计数结构进行分类。我们还证明，希尔伯特立方体同态同态的共轭等效关系对于通用轨道等效关系而言是borel的。
We study the complexity of the classification problem of conjugacy on dynamical systems on some compact metrizable spaces. Especially we prove that the conjugacy equivalence relation of interval dynamical systems is Borel bireducible to isomorphism equivalence relation of countable graphs. This solves a special case of the Hjorth's conjecture which states that every orbit equivalence relation induced by a continuous action of the group of all homeomorphisms of the closed unit interval is classifiable by countable structures. We also prove that conjugacy equivalence relation of Hilbert cube homeomorphisms is Borel bireducible to the universal orbit equivalence relation.
