题目1： Density and stability of ergodicity among partially hyperbolic diffeomorphisms（I）

报告人 Sylvain Crovisier（巴黎南大学，CNRS研究员，曾经在Annals of Math.，Invent. Math. 等顶级数学期刊发表论文若干篇，2014年被邀请至数学家大会作45分钟的分组报告）

报告时间：2015.12.05 09:00-09:50

 
报告地点：维格堂319

 
摘要：A mathematical formulation of Boltzmann‘s Ergodic Hypothesis in thermodynamics asserts that ergodicity should be ``the general case" in conservative dynamics. From KAM theory it is known that this hypothesis fails, but it is expected to be true for systems exhibiting a weak form of  hyperbolicity.
 We will present two results about the dynamics of volume-preserving diffeomorphisms, obtained with Artur Avila and Amie Wilkinson.




 

 
题目2：Density and stability of ergodicity among partially hyperbolic diffeomorphisms（II）

报告人 Sylvain Crovisier（巴黎南大学，CNRS研究员，曾经在Annals of Math.，Invent. Math. 等顶级数学期刊发表论文若干篇，2014年被邀请至数学家大会作45分钟的分组报告）

报告时间：2015.12.05 10:00-10:50

 
报告地点：维格堂319

 
摘要：we establish a dichotomy for C1-generic conservative diffeomorphisms: either the Lyapunov exponents of almost-every orbit vanish, or the volume is ergodic and non-uniformly hyperbolic.





 
题目3：Density and stability of ergodicity among partially hyperbolic diffeomorphisms（III）

报告人 Sylvain Crovisier（巴黎南大学，CNRS研究员，曾经在Annals of Math.，Invent. Math. 等顶级数学期刊发表论文若干篇，2014年被邀请至数学家大会作45分钟的分组报告）

报告时间：2015.12.05 11:00-11:50

 
报告地点：维格堂319

 
摘要：we prove that stably ergodic diffeomorphisms are C1-dense among volume-preserving partially hyperbolic C2-diffeomorphisms, with any central dimension. This answers for the C1-topology a conjecture of Pugh and Shub. The argument is based on perturbations of horseshoes with large entropy.