SMOOTH SYMMETRIES OF ×a-INVARIANT SETS

Michael Hochman

doi:10.3934/jmd.2018017

SMOOTH SYMMETRIES OF ×a-INVARIANT SETS

Michael Hochman^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We study the smooth self-maps f of ×a-invariant sets X ⊆[0,1]. Under various assumptions we show that this forces log f ⁰(x)/ log a ∈ Q at many points in X. Our method combines scenery flow methods and equidistribution results in the positive entropy case, where we improve previous work of the author and Shmerkin, with a new topological variant of the scenery flow which applies in the zero-entropy case.

Original language	English
Pages (from-to)	187-197
Number of pages	11
Journal	Journal of Modern Dynamics
Volume	13
DOIs	https://doi.org/10.3934/jmd.2018017
State	Published - 2018

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Publisher Copyright:
© 2018 American Institute of Mathematical Sciences. All rights reserved.

Keywords

Fractal geometry
Hausdorff dimension
expanding maps
jointly invariant sets
measure rigidity

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10.3934/jmd.2018017

Cite this

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KW - expanding maps

KW - jointly invariant sets

KW - measure rigidity

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SMOOTH SYMMETRIES OF ×a-INVARIANT SETS

Abstract

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Keywords

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