Dynamical Systems Seminar | Scott Schmieding (Penn State University)

Title: Inertness and joint invariance for automorphisms of the shift

Abstract: An old question concerns what kinds of dynamics can commute with a shift of finite type (SFT). I'll discuss some recent work on this topic, joint with Bryna Kra, where we prove that inertness, a classical but mysterious property of automorphisms of an SFT, implies a certain joint invariance property. One consequence is that any system that commutes with a full shift on a prime number of symbols must have a nontrivial jointly invariant infinite compact subset. I'll also mention some other applications of this result.

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