题目：Robust historic behavior of generic orbits for heterodimensional cycles
报告人： Shin KIRIKI (Tokai University)
时间：2018年12月3日下午2：00-3：00
地点: 数学楼三楼教室 摘要：The theme of this study is non-hyperbolic dynamical systems and historic behavior,
 where non-hyperbolic dynamical systems exactly refer to diffeomorphisms having heterodimensional cycles,
 and historic behavior means a phenomenon of the absence of Birkhoff time averages for orbits with respect 
to the Lebesgue measure. We show that arbitraily $C^1$-close to any diffeomorphism $f$ with co-index 1 
heterodimensional cycles, there is a diffeomorphism which has a homoclinic class containing saddles of
 different indices and such that every orbit of generic subset of the homoclinic class has $C^1$-robust
 historic behavior. This is joint work with Y. Nakano and T. Soma.    
题目：Persistent super-polynomial emergence for homoclinic tangencies
报告人：Yushi Nakano  (Tokai University)
时间：2018年12月3日下午3：00-4：00
地点: 数学楼三楼教室
摘要：Emergence at scale $\epsilon$ is the minimal number of probability measures to describe the orbit of
 the dynamics ``by means of statistics'' with precision $\epsilon$. So, fast growth of emergence means 
irregular behaviour in the sense of Birkhoff’s ergodic theorem (called historic behaviour). It has 
recently been realized that a positive Lebesgue measure set of points with historic behaviour (persistently)
 appears for complicated dynamical systems, such as dynamical systems with heteroclinic connections or
 homoclinic tangencies. However, for all known results, growth rate of emergence is at most polynomial, 
and P. Berger conjectured that there are ``many'' dynamical systems with super-polynomial emergence. 
In this talk, I will give an affirmative answer to a version of Berger's conjecture: by arbitrary
 small perturbation of dynamical systems with persistent homoclinic tangencies, one can construct
 a positive Lebesgue measure set consisting of points with super-polynomial emergence. This is 
joint work with S. Kiriki and T. Soma.

题目：EQUILIBRIUM MEASURES FOR SOME PARTIALLY HYPERBOLIC SYSTEMS
报告人：Zelerowicz Agnieszka (Pennsylvania State University)
时间：2018年12月3日下午4：00-5:00
地点: 数学楼三楼教室
摘要：In this joint work with Vaughn Climenhaga and Yakov Pesin we study thermodynamic formalism for
 topologically transitive partially hyperbolic systems in which the center-stable bundle is integrable 
and nonexpanding, and show that every potential function satisfying the Bowen property has a unique 
equilibrium measure. Our method is to use tools from geometric measure theory to construct a suitable 
family of reference measures on unstable leaves as a dynamical analogue of Hausdorff measure, and then 
show that the averaged pushforwards of these measures converge to a measure that has the Gibbs property
 and is the unique equilibrium measure.