Hamilton系统给定能量闸轨道的多重性问题

Multiplicity problems of brake orbits with prescribed energy in Hamiltonian systems

闸轨道的多重性和稳定性是Hamilton系统中重要的研究问题,辛道路的Maslov型指标理论正是研究这类问题的有力工具.这篇综述文章简要介绍闸轨道边值辛道路的Maslov型指标理论及其迭代理论.作为应用,本文证明Seifert猜想在偶凸情形成立.最后介绍与闸轨道相关的最小周期问题和稳定性问题.

Multiplicity and stability of brake orbits are important problems in the study of Hamiltonian systems,while the Maslov-type index theory and its iteration theory are the powerful tools to study such problems. In this survey paper, we briefly introduce the brake orbit boundary valued Maslov-type index theory and its iteration theory. As an application, we prove that Seifert conjecture holds in the even convex case. At the end of this paper we introduce the minimal period problem and stability problems related to brake orbits.