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arXiv · 2409.14962

The number of periodic points of surface symplectic diffeomorphisms

Marcelo S. Atallah·Marta Batoréo·Brayan Ferreira
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Abstract

We use symplectic tools to establish a smooth variant of Franks theorem for a closed orientable surface of positive genus $g$; it implies that a symplectic diffeomorphism isotopic to the identity with more than $2g-2$ fixed points, counted homologically, has infinitely many periodic points. Furthermore, we present examples of symplectic diffeomorphisms with a prescribed number of periodic points. In particular, we construct symplectic flows on surfaces possessing only one fixed point and no other periodic orbits.

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Marcelo S. Atallah, Marta Batoréo, Brayan Ferreira. 2024-09-23. The number of periodic points of surface symplectic diffeomorphisms. https://arxiv.org/abs/2409.14962

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