Abstract:We investigate generic properties (i.e. properties corresponding to residual sets) in the space of subshifts with the Hausdorff metric. Our results deal with four spaces: the space S of all subshifts, the space S ′ of non-isolated subshifts, the closure T ′ of the infinite transitive subshifts, and the closure TT ′ of the infinite totally transitive subshifts.In the first two settings, we prove that generic subshifts are fairly degenerate; for instance, all points in a generic subshift are biasymptotic to peri… Show more
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