Monotone quotients of surface diffeomorphisms
André de Carvalho, Miguel Paternain
Abstract
A homeomorphism of a compact metric space is tight provided every non-degenerate compact connected (not necessarily invariant) subset carries positive entropy. It is shown that every C1+α diffeomorphism of a closed surface factors to a tight homeomorphism of a generalized cactoid (roughly, a surface with nodes) by a semi-conjugacy whose fibers carry zero entropy.
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