Another dichotomy for surface diffeomorphisms

Morales, C.

doi:10.1090/S0002-9939-09-09879-7

Another dichotomy for surface diffeomorphisms
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Proc. Amer. Math. Soc. 137 (2009), 2639-2644 Request permission

Abstract:

We prove that a $C^1$ generic orientation-preserving diffeomorphism of a closed orientable surface either has infinitely many periodic points with complex (nonreal) eigenvalues or is Axiom A without cycles. This improves Mañé’s dichotomy.

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