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Remarks on periodic points, flux, and the mean index in symplectic dynamics
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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BibTeX
@misc{atallah2026remarks,
title = {{Remarks on periodic points, flux, and the mean index in symplectic dynamics}},
author = {Marcelo S. Atallah and Marta Batoréo and Brayan Ferreira},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02539},
eprint = {2610.02539},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02539},
}
RIS
TY - UNPB
TI - Remarks on periodic points, flux, and the mean index in symplectic dynamics
AU - Marcelo S. Atallah
AU - Marta Batoréo
AU - Brayan Ferreira
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02539
UR - https://arxiv.org/abs/2610.02539
AB - 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.
ER -