Ergodic Theory/Probability Seminar - Yun Yang

Title: Random perturbations of predominantly expanding multimodal circle maps

Speaker: Yun Yang (CUNY)

Abstract: In this talk we will study the effects of IID random perturbations of amplitude $\epsilon > 0$ on the asymptotic dynamics of one-parameter families $\{f_a : S^1 \to S^1, a \in [0,1]\}$ of smooth multimodal maps which ``predominantly expanding'', i.e., $|f'_a| \gg 1$ away from small neighborhoods of the critical set $\{ f'_a = 0 \}$. We will obtain, for any $\epsilon > 0$, a checkable, finite-time criterion on the parameter $a$ for random perturbations of the map $f_a$ to exhibit (i) a unique stationary measure, and (ii) a positive Lyapunov exponent comparable to $\int_{S^1} \log |f_a'| \, dx$.