Computation of annular capacity by Hamiltonian Floer theory of non-contractible periodic trajectories
Computation of annular capacity by Hamiltonian Floer theory of non-contractible periodic trajectories
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DOI：
10.3934/jmd.2017013
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发表时间：
2017-03
期刊：
影响因子：
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通讯作者：
Morimichi Kawasaki;Ryuma Orita
中科院分区：
文献类型：
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作者：
Morimichi Kawasaki;Ryuma Orita
第一作者引入了辛流形$(N,\omega_N)$及其子集$X$的相对辛容量$C$，该相对辛容量用于测量在$N$与环空$A_R=(R，R)\乘以\mathbb{R}/\mathbb{Z}$积上哈密顿同位素的不可收缩周期轨迹的存在性。本文给出了2n环面$\mathbb{T}^{2n}$相对于拉格朗日子流形$\mathbb{T}^n$的容量$C$的精确计算，该容量$C$暗示了在$A_R\乘以\mathbb{T}^{2n}$上存在不可收缩的哈密顿周期轨迹。此外，我们给出了这类轨迹数目的下界。
The first author introduced a relative symplectic capacity $C$ for a symplectic manifold $(N,\omega_N)$ and its subset $X$ which measures the existence of non-contractible periodic trajectories of Hamiltonian isotopies on the product of $N$ with the annulus $A_R=(R,R)\times\mathbb{R}/\mathbb{Z}$. In the present paper, we give an exact computation of the capacity $C$ of the $2n$-torus $\mathbb{T}^{2n}$ relative to a Lagrangian submanifold $\mathbb{T}^n$ which implies the existence of non-contractible Hamiltonian periodic trajectories on $A_R\times\mathbb{T}^{2n}$. Moreover, we give a lower bound on the number of such trajectories.