Dimension of ergodic measures projected onto self-similar sets with overlap

Thomas Jordan, Ariel Rapaport

Research output: Contribution to journalArticle (Academic Journal)peer-review

8 Citations (Scopus)
77 Downloads (Pure)

Abstract

For self-similar sets on R satisfying the exponential separation condition we show that the dimension of natural projections of shift invariant ergodic measures is equal to min{1, h−χ}, where h and χ are the entropy and Lyapunov exponent respectively. The proof relies on Shmerkin’s recent result on the Lq dimension of self-similar measures. We also use the same method to give results on convolutions and orthogonal projections of ergodic measures projected onto self-similar sets.
Original languageEnglish
Pages (from-to)191-206
Number of pages16
JournalProceedings of the London Mathematical Society
Volume122
Issue number2
Early online date29 Apr 2020
DOIs
Publication statusPublished - 1 Feb 2021

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