Fixed point shifts of inert involutions (Q1045783)

For a mixing shift of finite type \(X\) is considered which subshifts of finite type \(Y\subset X\) can be realized as the fixed point shift of an inert involution of \(X\). A condition on the periodic points of \(X\) and \(Y\) that is necessary for \(Y\) to be fixed point shift of an inert involution of \(X\) is stated. Is showed that this condition is sufficient to realize \(Y\) as the fixed point shift of involution, up to shift equivalence on \(X\), if \(X\) is a shift of finite type with Artin-Mazur zeta function equivalent to 1 and 2. What \(f\)-invariant subshifts which can be realized as the fixed point shift of an inert involution are characterized for an inert involution \(f\).