Structure and f-dependence of the a.c.i.m. for a unimodal map f of Misiurewicz type

Perturbing Misiurewicz parameters in the exponential family

In one-dimensional real and complex dynamics, a map whose post-singular (or post-critical) set is bounded and uniformly repelling is often called a Misiurewicz map. In results hitherto, perturbing a Misiurewicz map is likely to give a non-hyperbolic map, as per Jakobson's Theorem for unimodal interval maps. This is despite genericity of hyperbolic parameters (at least in the interval setting). We show the contrary holds in the complex exponential family $z \mapsto λ\exp(z)$: Misiurewicz maps are Lebesgue density points for hyperbolic parameters. As a by-product, we also show that Lyapunov expo…

一类单峰映射击中时间与逃逸速率的三元划分

A trichotomy for hitting times and escape rates for a class of unimodal maps

本文研究了一类单峰映射中击中时间与逃逸速率的三元划分，揭示了周期点在后临界轨道上的特性，并证明了广义渐近逃逸速率的性质。