Abstract

In this talk, the concepts of multiplicative subshifts and its dimensions are introduced. Kenyon, Peres and Solomyak [Ergod. Th. Dynam. Sys., 2012] obtained the Minkowski and Hausdorff dimensions of multiplicative subshifts which is the special type of multiple ergodic average. Later, Fan, Schmeling and Wu [Adv. Math, 2016] obtained the multifractal analysis of multiple ergodic averages. Ban, Hu and Lai [Ergod. Th. Dynam. Sys., 2023] extended the Kenyon et al. and Fan et al. results to multidimensional version. Recently, we extend the Kenyon et al. results to affine multiplicative subshifts.

 

Organizers: Kuan-Wei Chen (NCTS) & Ryota Mikami (AS)