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The scenery flow of self-similar measures with weak separation condition

Published online by Cambridge University Press:  06 August 2021

ALEKSI PYÖRÄLÄ*
Affiliation:
Research Unit of Mathematical Sciences, University of Oulu, PO Box 8000, FI-90014, Oulu, Finland

Abstract

We show that self-similar measures on $\mathbb R^d$ satisfying the weak separation condition are uniformly scaling. Our approach combines elementary ergodic theory with geometric analysis of the structure given by the weak separation condition.

Type
Original Article
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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