Equilibrium states of affine iterated function systems

Ian Morris (University of Surrey)

Frank Adams 1,

The dimension theory of self-similar fractals has been well-understood since the 1980s, at least in cases where the similarities have non-overlapping images. In the dimension theory of self-affine fractals, on the other hand, many questions remain open. I will describe some of my recent work with Jairo Bochi and Antti Kaenmaki on the equilibrium states of affine iterated function systems and its implications for the dimension theory of self-affine sets.

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