Dimension of invariant measures for affine iterated function systems

De-Jun Feng
The Chinese University of Hong Kong

Date(s) : 24/10/2017   iCal
11 h 00 min - 12 h 00 min

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.



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