Characterization of inert actions on periodic points. Part I

This article together with [KRW3] characterizes the action of inert automor phisms on finite sets of periodic points of mixing subshifts of finite type in terms of the sign-gyration-compatibility-condition. The main technique used is variable length coding combined with an algebraic K-theory formulat ion of state splitting and merging. Together with the work of Boyle-Fiebig [BF], the Inert Action Theorem gives counterexamples to the FOG Conjecture by producing examples of infinite order inert automorphisms of mixing subsh ifts of finite type which are not products of finite order automorphisms.