Ergodic theory for vector fields with singularities

主讲人：杨大伟  苏州大学教授

时间：2021年11月8日19：45

地点：腾讯会议 524 306 310

举办单位：数理学院

内容介绍：We study vector fields with singularities from the viewpoint of ergodic theory.  One important prototype is the Lorenz attractor. Theoretical notions for the  weak hyperbolicity of vector fields with singularites include singular  hyperbolicity and multi-singular hyperbolicity. Sinai-Ruelle-Bowen measures are  generally one the most interesting measures to characterize the ergodic  properties of attractors. Our main results are the existence and finiteness of  SRB measures for most singular hyperbolic vector fields and multi-singular  vector fields. The technics involve thermodynamical formalism, C^\infty tricks,  blow-ups, generic arguments and Liao's canonical equations.