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arXiv · 2103.08938

A short proof of Host's equidistribution theorem

Michael Hochman
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Abstract

This note contains a new proof of Host's equidistribution theorem for multiplicatively independent endomorphisms of $\mathbb{R}/\mathbb{Z}$. The method is a simplified version of our upcoming work on equidistribution under toral automorphisms and is related to the argument in [HochmanShmerkin2015], but avoids the use of the scenery flow and of Marstrand's projection theorem, using instead a direct Fourier argument to establish smoothness of the limit measure.

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Michael Hochman. 2021-03-16. A short proof of Host's equidistribution theorem. https://doi.org/10.1007/s11856-022-2444-x

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