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 language | English |
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Pages (from-to) | 191-206 |
Number of pages | 16 |
Journal | Proceedings of the London Mathematical Society |
Volume | 122 |
Issue number | 2 |
Early online date | 29 Apr 2020 |
DOIs | |
Publication status | Published - 1 Feb 2021 |
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Dr Thomas M Jordan
- Probability, Analysis and Dynamics
- School of Mathematics - Senior Lecturer in Pure Mathematics
- Pure Mathematics
- Ergodic theory and dynamical systems
Person: Academic , Member