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Fixed point shifts of inert involutions

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  • Given a mixing shift of finite type $X$, we consider which subshifts of finite type $Y \subset X$ can be realized as the fixed point shift of an inert involution of $X$. We establish a condition on the periodic points of $X$ and $Y$ that is necessary for $Y$ to be the fixed point shift of an inert involution of $X$. We show that this condition is sufficient to realize $Y$ as the fixed point shift of an involution, up to shift equivalence on $X$, if $X$ is a shift of finite type with Artin-Mazur zeta function equivalent to 1 mod 2. Given an inert involution $f$ of a mixing shift of finite type $X$, we characterize what $f$-invariant subshifts can be realized as the fixed point shift of an inert involution.
    Mathematics Subject Classification: Primary: 37B10; Secondary: 37C85, 37F10.

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