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

Part of: Ergodic theory Measure-theoretic ergodic theory Classical measure theory

Published online by Cambridge University Press:  06 August 2021

ALEKSI PYÖRÄLÄ Open the ORCID record for ALEKSI PYÖRÄLÄ [Opens in a new window]
ALEKSI PYÖRÄLÄ*
Affiliation:
Research Unit of Mathematical Sciences, University of Oulu, PO Box 8000, FI-90014, Oulu, Finland
*
e-mail: [email protected]
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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.

Keywords

scenery flowself-similar measureweak separation conditionuniformly scaling measure

MSC classification

Primary: 37A10: One-parameter continuous families of measure-preserving transformations
Secondary: 28A80: Fractals 28D05: Measure-preserving transformations
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 10 , October 2022 , pp. 3167 - 3190
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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