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