December  2009, 25(4): 1297-1317. doi: 10.3934/dcds.2009.25.1297

Fixed point shifts of inert involutions


Stephen F. Austin State University, Department of Mathematics and Statistics, P.O. Box 13040, SFA Station, Nacogdoches, TX 75962-3040, United States

Received  February 2009 Revised  June 2009 Published  September 2009

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.
Citation: Nicholas Long. Fixed point shifts of inert involutions. Discrete & Continuous Dynamical Systems, 2009, 25 (4) : 1297-1317. doi: 10.3934/dcds.2009.25.1297

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