Inert actions on periodic points

Abstract

The action of inert automorphisms on finite sets of periodic points of mixing subshifts of finite type is characterized in terms of the sign-gyration-compatibility condition. The main technique used is variable length coding combined with a “nonnegative algebraic K-theory" formulation of state splitting and merging. One application gives a counterexample to the Finite Order Generation Conjecture by producing examples of infinite order inert automorphisms of mixing subshifts of finite type which are not products of finite order automorphisms.