动力系统讨论班——A rescaled expansiveness for flows
主 题: 动力系统讨论班——A rescaled expansiveness for flows
报告人: 文晓 (北京航空航天大学)
时 间: 2017-10-25 15:10-17:10
地 点: 二教408
Abstract: We introduce a new version of expansiveness for flows. Let M be a compact Rie-mannian manifold without boundary and X be a C1 vector eld on M that generates a flow φt on M. We call X rescaling expansive on a compact invariant set ∧ of X if for any € > 0 there is δ> 0 such that, for any x; y ∈∧ and any time reparametrization θ : R→ R, if d(φt(x); φ(t)(y)) ≤δ ∥X(φt(x))∥ for all t ∈ R, then φ(t)(y)∈φ[-€;€](φt(x)) for all t ∈ R. We prove that every multisingular hyperbolic set (singular hyperbolic set in particular) is rescaling expansive and a converse holds generically. This is a joint work with Lan Wen.