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arXiv · 2610.02539

Remarks on periodic points, flux, and the mean index in symplectic dynamics

Marcelo S. Atallah·Marta Batoréo·Brayan Ferreira
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Abstract

It is shown that a symplectic isotopy with non-degenerate end-point on a closed symplectically Calabi--Yau manifold has simple periodic points of arbitrarily large period under a simple non-vanishing condition on the Morse--Novikov homology associated with its flux. The proof combines a sharp estimate for the Conley--Zehnder index under the assumption that the mean index is an even integer with a classical asymptotic iteration argument in the non-Hamiltonian Floer-theoretic setting. We also apply this estimate to the symplectic dynamics of the standard symplectic $4$-torus.

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Marcelo S. Atallah, Marta Batoréo, Brayan Ferreira. 2026-10-01. Remarks on periodic points, flux, and the mean index in symplectic dynamics. https://arxiv.org/abs/2610.02539

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