报告人  Jerome Buzzi（Universite de Paris-Sud，CNRS研究员）

报告时间 2017年3月26日09:30-10:30

报告地点  维格堂319

报告摘要   Markov shifts and their finite-to-one factors have the same type of measures maximizing the entropy.  However more structure is necessary to control other measures. We introduce a simple such property which we call the Bowen property since it was first used by Bowen in his study of the Markov partitions for uniformly hyperbolic dynamics. We show that finite-to-one Bowen factors of Markov shfts are isomorphic to Markov shifts, up to periodic measures by using a Borel generator theorem of Hochman (2014). Using Sarig's coding, this yields a classification of surface diffeomorphisms. The Bowen property allows to define a notion of degree that improves the lower bound on the number of hyperbolic periodic points for surface diffeomorphisms with measures maximizing the entropy.

In this first talk, we will give some introductions of this topic.

报告人  Jerome Buzzi（Universite de Paris-Sud，CNRS研究员）

报告时间 2017年3月26日10:30-11:30

报告地点  维格堂319

报告摘要   In the second talk we first classify Markov shifts and characterize them as strictly universal with respect to a natural family of classes of Borel systems. We then study their continuous factors showing that a low entropy part is almost-Borel isomorphic to a Markov shift but that the remaining part is much more diverse, even for finite-to-one factors. However, we exhibit a new condition which we call ‘Bowen type’ which gives complete control of those factors.

报告人  Jerome Buzzi（Universite de Paris-Sud，CNRS研究员）

报告时间 2017年3月26日11:30-12:30

报告地点  维格堂319

报告摘要  This result in the second talk applies to and was motivated by the symbolic covers of Sarig. We find complete numeric invariants for Borel isomorphism of C1+ surface diffeomorphisms modulo zero entropy measures; for those admitting a totally ergodic measure of positive (not necessarily maximal) entropy, we get a classification up to almost-Borel isomorphism.