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Inert actions on periodic points. (English) Zbl 0881.54042

Summary: 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.

MSC:

54H20 Topological dynamics (MSC2010)
57S99 Topological transformation groups
20F99 Special aspects of infinite or finite groups
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