%0 Journal Article
%T Monotone quotients of surface diffeomorphisms
%A Andr¨¦ de Carvalho
%A Miguel Paternain
%J Mathematics
%D 2002
%I arXiv
%X A homeomorphism of a compact metric space is {\em tight} provided every non-degenerate compact connected (not necessarily invariant) subset carries positive entropy. It is shown that every $C^{1+\alpha}$ 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.
%U http://arxiv.org/abs/math/0211050v1