Homeomorphisms of One-dimensional Inverse Limits with Applications to Substitution Tilings, Unstable Manifolds, and Tent Maps
نویسنده
چکیده
Suppose that f and g are Markov surjections, each defined on a wedge of circles, each fixing the branch point and having the branch point as the only critical value. We show that if the points in the inverse limit spaces associated with f and g corresponding to the branch point are distinguished then these inverse limit spaces are homeomorphic if and only if the substitutions associated with f and g are weakly equivalent. This, and related results, are applied to one-dimensional substitution tiling spaces, one-dimensional unstable manifolds of hyperbolic sets, and inverse limits of tent maps with periodic critical points.
منابع مشابه
Homeomorphisms of inverse limit spaces of one-dimensional maps
We present a new technique for showing that inverse limit spaces of certain one-dimensional Markov maps are not homeomorphic. In particular, the inverse limit spaces for the three maps from the tent family having periodic kneading sequence of length five are not homeomorphic.
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