ncts

News

Events

Directors

International Advisory Committee

Executive Committee

Academic Committee & Related

Sponsored by

Events

News

[ Events ]

Seminars and Talks

Conferences, Workshops and Special Events

Courses and Lecture Series

Taiwan Math. School

Activity Search

Sort out

Field

Year

．Seminars

	European-Asian Joint Webinar on Dynamical Systems

16:00 - 17:30, May 17, 2022 (Tuesday)
Zoom, Online seminar
(線上演講 Zoom)
Uniform Approximation Problems of Expanding Markov Map
Yubin He (South China University of Technology)

Abstract

Let $T$ be an expanding Markov map of the interval $[0,1]$ with a finite partition. Let $\mu_{\phi}$ be an invariant Gibbs measure associated with a Hölder continuous potential $\phi$ . In this talk, we investigate the size of the uniform approximation set

$\mathcal{U}^{\kappa}(x):=\{y \in [0, 1]: \forall N \gg 1,~\exists n \leq N, \text{ such that } |T^n x - y| < N^{-\kappa}\},$ where $\kappa > 0$ and $x \in [0, 1]$ . The critical value of $\kappa$ such that $\dim_H \mathcal{U}^{\kappa}(x) = 1$ for $\mu_{\phi}$-a.e.~$x$ is proven to be $1/\alpha_{\max}$ , where $\alpha_{\max} = \int -\phi d\mu_{\max} / \int \log |T'| d \mu_{\max}$ and $\mu_{\max}$ is the Gibbs measure associated with the potential $-\log |T'|$ . Moreover, when $\kappa$ >1/ $\alpha_{\max}$ , we show that for $\mu_{\phi}$ -a.e.~ $x$ , the Hausdorff dimension of $\mathcal{U}^{\kappa}(x)$ agrees with the multifractal spectrum of $\mu_{\phi}$ .

Meeting Link

https://us02web.zoom.us/j/82058526043?pwd=Z0QzVXZVNDRTRkhJMG4rQ0dlSlkzUT09