报告题目：Multifractal analysis of Birkhoff averages

报告人：廖灵敏教授（Universit´e Paris-Est Cr´eteil）

报告时间：2013年7月5日（星期五）下午3：30

报告地点：数学楼二楼学术报告厅

Abstract：In a dynamical system, for a given observation, we consider the level sets of its Birkhoff averages. Multifractal analysis of Birkhoff averages aims to determine the function from the levels to the sizes (Hausdorff or entropy) of the corresponding level sets which is usually called the multifractal spectrum of the Birkhoff averages. A classical example is the determination of the Hausdorff dimension of the sets of points with prescribed digit frequencies in its m-adic expansions. This talk is mainly concerned with some mutifractal spectra in the Gauss dynamical system associated to continued fractions. Among others, the multifractal spectra of the Khinchine exponents and Lyapunov exponents of continued fractions are given. The frequencies of the digits in continued fractions are studied. A generalization to interval maps of infinitely many branches will be presented. If time permits, some recent developments on the multifractal analysis of multiple ergodic averages will also be mentioned.

(数学科学学院)