Konrad Deka (Jagiellonian University, Cracow) скачать в хорошем качестве

Konrad Deka (Jagiellonian University, Cracow)

Title: The relation of topological conjugacy of Cantor minimal systems is not Borel Abstract: The notion of Borel reducibility, developed mainly by descriptive set theorists, is a tool for measuring the complexity of an equivalence relation. Given a class of mathematical objects, it can usually be applied to study the isomorphism relation between those objects. In 2011, Foreman, Rudolph and Weiss showed that the conjugacy of of ergodic MPS (measure-preserving systems) is not Borel. The result can be interpreted as proof of non-existence of certain simpler descriptions of when two ergodic MPS are isomorphic (for example, no complete invariant exists). Several other classes of topological and measurable dynamical systems have also been studied in a similar manner. We will provide an introduction to the topic of Borel reducibility, survey the results related to dynamical systems, and discuss some new results.