数学所周五学术报告—Weak hyperbolic structures and robust properties of diffeomorphisms and flows
主 题: 数学所周五学术报告—Weak hyperbolic structures and robust properties of diffeomorphisms and flows
报告人: Professor Christian Bonatti (Bourgogne University, France)
时 间: 2017-04-28 16:30-17:30
地 点: 理科1号楼1114
Abstract: A dynamical property is called robust if its holds on a (non-empty) open set of diffeomorphisms or flows. This means that it is impossible to break the property by small perturbations. It is therefore natural that robust properties are strongly related with structures limitating the effect of small perturbations.
Several of these structures (hyperbolicity, partial hyperbolicity, dominated splitting, ...) are now classical for diffeomorphisms or for nonsingular flows. In this talk, as a joint work with A. da Luz, we will propose a way for extending these structures to singularities of flows. We will illustrate the strength of this notion with the case of the star flows, that is, the flows for which, robustly, all the periodic orbits are hyperbolic.