Full paper in PDF format:
$% M. J. Pacifico and J. L. Vieitez, Entropy-expansiveness and domination
for surface diffeomorphisms, Rev. Mat. Complut. 21 (2008), no. 2, 293–317.%$
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ABSTRACT
Let be a -diffeomorphism, , defined on a closed manifold . We prove that if is a surface and is a compact invariant set such that is a dominated splitting then is entropy expansive. Moreover generically in any dimension, isolated homoclinic classes , hyperbolic, are entropy expansive.
Conversely, if there exists a neighborhood of a surface diffeomorphism and a homoclinic class , hyperbolic, such that for every the continuation of is entropy-expansive then there is a dominated splitting for .
Key words: entropy-expansiveness, homoclinic classes, dominated splitting, homoclinic
tangency, symbolic extension.
2000 Mathematics Subject Classification: 37D30, 37C29, 37E30.