发表机构
Universidade de São Paulo; Universidade Federal do Espírito Santo（圣保罗大学; 圣埃斯皮里图联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明闭辛Calabi-Yau流形上非退化端点辛同伦在通量相关同调非消失条件下具有任意大周期简单周期点，并应用于标准辛4-环面。
AI 中文摘要
本文证明了在闭的辛Calabi-Yau流形上，若辛同伦的端点非退化，且其通量相关的Morse-Novikov同调满足简单的非消失条件，则该同伦具有任意大周期的简单周期点。证明结合了在平均指标为偶整数假设下对Conley-Zehnder指标的尖锐估计，以及非哈密顿Floer理论框架中的经典渐近迭代论证。我们还将此估计应用于标准辛$4$-环面的辛动力学。
英文摘要
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.
Comments10 pages
