On the structure of generic subshifts

Abstract We investigate generic properties (i.e. corresponding to residual sets) in the space of subshifts with Hausdorff metric. Our results deal four spaces: S all subshifts, S mathvariant="normal">′ non-isolated closure $\overline{\mathbf{T}^{^{\prime}}}$?> mathvariant="bold">T ‾ infinite transitive and $\overline{\mathbf{T}\mathbf{T}^{^{\prime}}}$?> totally subshifts. In first two settings, we prove that are fairly degenerate; for instance, points a subshift biasymptotic periodic orbits. contrast, latter spaces possess more interesting dynamical behavior. Notably, both zero entropy, minimal, uniquely ergodic, have word complexity which realizes any possible subexponential growth rate along subsequence. addition, is regular Toeplitz strongly orbit equivalent universal odometer.