（一）报告人：Katsutoshi Shinohara (Hitotsubashi University)

报告题目：Growth of number of periodic points and hyperbolicity

报告摘要：I will discuss the relation between the growth of number of periodic points and hyperbolicity.More precisely, I will talk about what one can say about the growth of number of periodic points for partially hyperbolic diffeomoprhisms.

报告时间：2018年11月10日（星期六）下午2:00-3:00

报告地点：科技楼南楼702室

（二）报告人：Yushi Nakano (Tokai University)

报告题目：Random historic behaviour for expanding maps

报告摘要：A point for a (random) dynamical system is said to have historic behaviour if for some continuous function on the state space, the time average does not exist (the point is also called a non-typical point or irregular point). The set of points with historic behaviour, called historic set, is a zero measure set for any invariant measure due to Birkhoff’s ergodic theorem. In this sense, historic set is not observable. However, rather recently, it was shown that observable historic set is not rare from other perspectives: (i) The historic sets of expanding maps are residual. (ii) The historic sets of diffeomorphisms in a dense subset of the Newhouse domain have positive Lebesgue measure.

In context of random dynamical systems, it was shown by V. Araujo that under small, absolute continuous, iid random perturbation, any historic set  is of zero Lebesgue measure. This means (together with (ii)) that the measure-theoretic observability of historic set disappears under small iid perturbation. In this talk, in strong contrast to it, I will show that the topological observability of historic set in the sense of (i) still appears under any small perturbation.

报告时间：2018年11月10日（星期六）下午3:00-4:00

报告地点：科技楼南楼702室

（三）报告人：Kenichiro Yamamoto (Nagaoga University of Technology)

报告题目：Intrinsic ergodicity for factors of (−β)-shifts

报告摘要：We proved that every subshift factor of a (−β)-shift is intrinsically ergodic, when β ≥ (1+√5)/2 and the (−β)-expansion of −1 is not periodic withodd period. Moreover, the unique measure of maximal entropy satisfies a certain Gibbs property. This is an application of the technique established by Climenhaga and Thompson to prove intrinsic ergodicity beyond specification. We also prove that there exists a subshift factor of a (−β)-shift which is not intrinsically ergodic in the cases other than the above. This is a joint work with M. Shinoda (Keio University).

报告时间：2018年11月10日（星期六）下午4:00-5:00

报告地点：科技楼南楼702室