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

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.