Wandering Triangles Exist
نویسنده
چکیده
W. P. Thurston introduced closed σd-invariant laminations (where σd = z : S → S, d ≥ 2) as a tool in complex dynamics. He defined wandering triangles as triples T ⊂ S such that σ d (T ) consists of three distinct points for all n ≥ 0 and the convex hulls of all the sets σ d (T ) in the plane are pairwise disjoint, and proved that σ2 admits no wandering triangles. We show that for every d ≥ 3 there exist uncountably many σd-invariant closed laminations with wandering triangles and pairwise non-conjugate factor maps of σd on the corresponding quotient spaces.
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