Radial projections along chains

Laurent Dufloux

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arXiv · 1901.07247

Radial projections along chains

Laurent Dufloux

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Abstract

We state strong Marstrand properties for two related families of fractals in Heisenberg groups $\mathcal{H}^d$: limit sets of Schottky groups in good position, and attractors of self-similar IFS enjoying the open set condition in the quotient $\mathcal{H}^d/Z$. For such a fractal $X$, we show that the dimension of $π_x X$ does not depend on $x \in \mathcal{H}^d$, where $π_x$ denotes the radial projection along chains passing through $x$. This follows from a local entropy averages argument due to Hochman and Shmerkin.

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BibTeX RIS

Laurent Dufloux. 2019-01-22. Radial projections along chains. https://arxiv.org/abs/1901.07247

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