Hofer-Zehnder semicapacity of cotangent bundles and symplectic submanifolds
| dc.creator | Macarini, Leonardo | |
| dc.date | 2003-03-19 | |
| dc.date | 2003-08-18 | |
| dc.date.accessioned | 2026-07-07T04:56:11Z | |
| dc.date.available | 2026-07-07T04:56:11Z | |
| dc.description | We introduce the concept of Hofer-Zehnder $G$-semicapacity (or $G$-sensitive Hofer-Zehnder capacity) and prove that given a geometrically bounded symplectic manifold $(M,ω)$ and an open subset $N \subset M$ endowed with a Hamiltonian free circle action $ϕ$ then $N$ has bounded Hofer-Zehnder $G_ϕ$-semicapacity, where $G_ϕ\subset π_1(N)$ is the subgroup generated by the homotopy class of the orbits of $ϕ$. In particular, $N$ has bounded Hofer-Zehnder capacity. We give two types of applications of the main result. Firstly, we prove that the cotangent bundle of a compact manifold endowed with a free circle action has bounded Hofer-Zehnder capacity. In particular, the cotangent bundle $T^*G$ of any compact Lie group $G$ has bounded Hofer-Zehnder capacity. Secondly, we consider Hamiltonian circle actions given by symplectic submanifolds. For instance, we prove the following generalization of a recent result of Ginzburg-Gürel: almost all low levels of a function on a geometrically bounded symplectic manifold carry contractible periodic orbits of the Hamiltonian flow, provided that the function attains its minimum along a closed symplectic submanifold. | |
| dc.description | 19 pages, 4 figures. Revised version | |
| dc.identifier | https://arxiv.org/abs/math/0303230 | |
| dc.identifier | http://arxiv.org/abs/math/0303230 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66832 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Dynamical Systems | |
| dc.title | Hofer-Zehnder semicapacity of cotangent bundles and symplectic submanifolds | |
| dc.type | text |