Mathematical Research Letters

Volume 10 (2003)

Number 5

Monotone quotients of surface diffeomorphisms

Pages: 603 – 619



André de Carvalho (SUNY)

Miguel Paternain (Facultad de Ciencias)


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.

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