EVENT DETAILS AND ABSTRACT

Title: Chaotic almost minimal systems
Speaker: Van Cyr
Speaker Info: Bucknell University
Brief Description:
Special Note:
Abstract:

A celebrated theorem of Furstenberg says that any closed subset of $S^1 = {\mathbb R}/{\mathbb Z}$ that is invariant under the maps $x \mapsto 2x \mod 1$ and $x \mapsto 3x \mod 1$ is either equal to $S^1$ or finite. There are many interesting things to ask about this system and a wide variety of questions remain open. In this talk, based on joint work with B. Kra and S. Schmeiding, I will introduce an abstraction of the $\times 2, \times 3$ system to what we call a chaotic almost minimal system. After providing definitions, I will survey some results on the interplay between the acting group and the kinds of phenomena that are possible.