论文标题
稳定的汉密尔顿结构的周期性轨道和伯克霍夫部分
Periodic orbits and Birkhoff sections of stable Hamiltonian structures
论文作者
论文摘要
稳定的汉密尔顿结构概括了接触形式，并定义了一个称为Reeb Vector Field的体积的矢量场。我们研究了由稳定的汉密尔顿结构定义的Reeb矢量场的两个方面：一方面，我们将所有例子与有限的周期性轨道分类为非分类条件下的所有例子；另一方面，我们为存在的损坏书籍分解和伯克霍夫部分的存在提供了足够的条件。
Stable Hamiltonian structures generalize contact forms and define a volume-preserving vector field known as the Reeb vector field. We study two aspects of Reeb vector fields defined by stable Hamiltonian structures on 3-manifolds: on one hand, we classify all the examples with finitely many periodic orbits under a non-degeneracy condition; on the other, we give sufficient conditions for the existence of a supporting broken book decomposition and for the existence of a Birkhoff section.
