Rigidity in one-dimensional tiling spaces

摘要

Suppose T_ψ and T_θ are tiling spaces arising from primitive nonperiodic substitutions ψ and θ Suppose F_ψ and F_θ denote the corresponding inflation and substitution maps on the respective tiling spaces. We prove that T_ψ and T_θ are homeomorphic if and only if there exist positive integers m and n such that F_ψ~n and F_θ~m are topologically conjugate.