# Dynamics seminar: Natalia Jurga (St. Andrews) Hausdorff dimension of self-projective sets

Abstract: A finite set of matrices $A \subset SL(2,R)$ acts on one-dimensional real projective space $RP^1$ through its linear action on $R^2$. In this talk we will be interested in the “projective attractor” of $A$: the smallest closed subset of $RP^1$ which contains all attracting and neutral fixed points of matrices belonging to the semigroup generated by $A$. Recently, Solomyak and Takahashi proved that if $A$ is uniformly hyperbolic and satisfies a Diophantine property, then the projective attractor has Hausdorff dimension equal to the minimum of 1 and the critical exponent. In this talk we will discuss an extension of their result beyond the uniformly hyperbolic setting. This is based on joint work with Argyrios Christodoulou.

## Date:

Tue, 26/10/2021 - 14:00 to 15:00

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