Title: Hausdorff dimension of self-projective sets
Speaker: Natalia Jurga
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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 limit set of $A$: the smallest closed subset of $RP^1$ which contains all attracting 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 invariant set 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: Tuesday, May 24, 2022