Haojie, Ren (Technion Israel): Hausdorff dimension of solenoidal attractors

Solenoidal attractors are fractal sets arising in skew product systems. In this talk, I will introduce their definition, provide a simple geometric description, and give a brief overview of their research history. I will then focus on a special class of skew product maps, discussing my works on the SRB measures and the solenoidal attractors induced by these maps. The proofs draw on Hochman’s entropy growth tools for convolutions and techniques from my recent collaboration with Shen. I will also introduce some open questions in the field.