论文标题
相对Hofer-Zehnder的容量和阳性符号同源性
Relative Hofer-Zehnder capacity and positive symplectic homology
论文作者
论文摘要
We study the relationship between a homological capacity $c_{\mathrm{SH}^+}(W)$ for Liouville domains $W$ defined using positive symplectic homology and the existence of periodic orbits for Hamiltonian systems on $W$: If the positive symplectic homology of $W$ is non-zero, then the capacity yields a finite upper bound to the $π_1$-sensitive相对于其骨骼，$ W $的Hofer-Zehnder容量和某些类别的hamiltonian差异性$ w $具有无限的许多非平凡的合同周期点。 En passant，我们在同源容量$ c _ {\ mathrm {sh}}}}（w）$的频谱容量上给出了$ w $的上限。讨论了这些陈述在cotangent捆绑包中的应用，并在附录中使用了Abbondandolo和Mazzucchelli的结果，在$ \ Mathbb r^3 $中，凸Riemannian两杆的Systoles在其中的单调性。
We study the relationship between a homological capacity $c_{\mathrm{SH}^+}(W)$ for Liouville domains $W$ defined using positive symplectic homology and the existence of periodic orbits for Hamiltonian systems on $W$: If the positive symplectic homology of $W$ is non-zero, then the capacity yields a finite upper bound to the $π_1$-sensitive Hofer-Zehnder capacity of $W$ relative to its skeleton and a certain class of Hamiltonian diffeomorphisms of $W$ has infinitely many non-trivial contractible periodic points. En passant, we give an upper bound for the spectral capacity of $W$ in terms of the homological capacity $c_{\mathrm{SH}}(W)$ defined using the full symplectic homology. Applications of these statements to cotangent bundles are discussed and use a result by Abbondandolo and Mazzucchelli in the appendix, where the monotonicity of systoles of convex Riemannian two-spheres in $\mathbb R^3$ is proved.
