André de Carvalho, Miguel Paternain
Published 2002-11-04Version 1
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.
Comments: 14 pages, 4 figures
Takens-type reconstruction theorems of one-sided dynamical systems on compact metric spaces
On μ-Compatible Metrics and Measurable Sensitivity
Every compact metric space that supports a positively expansive homeomorphism is finite
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