Seminar 9.6.18 Yang

Title: Random perturbations of predominantly expanding multimodal circle maps

SpeakerYun Yang (CUNY)

Abstract: In this talk we will study the effects of IID random perturbations of amplitude ϵ>0 on the asymptotic dynamics of one-parameter families {fa:S1S1,a[0,1]of smooth multimodal maps which “predominantly expanding”, i.e., |fa|away from small neighborhoods of the critical set {fa=0}. We will obtain, for any ϵ>0, a checkable, finite-time criterion on the parameter aa for random perturbations of the map fafa to exhibit (i) a unique stationary measure, and (ii) a positive Lyapunov exponent comparable to S1log|fa|dx.