Dimension of invariant measures for affine iterated function systems
De-Jun Feng
The Chinese University of Hong Kong
https://www.math.cuhk.edu.hk/~djfeng/
Date(s) : 24/10/2017 iCal
11h00 - 12h00
In this talk, we investigate the local dimensions of certain fractal measures. We prove the exact dimensionality of ergodic invariant measures for every contractive affine iterated function systems. These measures are the push-forwards of the ergodic invariant measures in the symbolic space under the coding map, and include all the self-affine measures. We also establish the Ledrappier-Young type dimension formula. Furthermore, the result extends to average contracting affine IFSs. This completes several previous results. Some applications are given to the dimension of self-affine sets and measures.
https://arxiv.org/abs/1901.01691
Catégories
