In this paper, we treat an open problem related to the number of periodic orbits of Hamiltonian diffeomorphisms on closed symplectic manifolds, the so-called (generic) Conley conjecture. The generic Conley conjecture states that generically Hamiltonian diffeomorphisms have infinitely many simple contractible periodic orbits. We prove the generic Conley conjecture for very wide classes of symplectic manifolds. Our proof is based on applications of the Birkhoff–Moser fixed point theorem and Floer homology theory.

中文翻译：

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关于一般康利猜想

在本文中，我们处理与闭辛流形上哈密顿微分同胚的周期轨道数相关的开放问题，即所谓的（一般）康利猜想。通用康利猜想指出，通用哈密顿微分同胚具有无限多个简单的可收缩周期轨道。我们证明了非常广泛的辛流形类别的通用康利猜想。我们的证明基于 Birkhoff-Moser 不动点定理和 Floer 同源理论的应用。