Projections of self-similar sets with no separation condition

Abel Farkas (University of St Andrews)

Frank Adams Room 1, Alan Turing Building,

We investigate how the Hausdorff dimension and measure of a self-similar set \(K \subseteq \mathbb{R}^d\) behave under linear images. It turns out that this depends on the nature of the
group generated by the orthogonal parts of defining maps of \(\)K. We prove our results
without assuming any separation condition. We introduce a new method that leads to a similarity dimension-like formula for Hausdorff dimension.
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