精品文档---下载后可任意编辑一次五类 Z2 等变近哈密顿系统的极限环分支的开题报告摘要：本文讨论了一类五类 Z2 等变近哈密顿系统的极限环分支。通过构造适当的极限环偏移函数，利用 KAM 理论和分岔理论分析了极限环分支的存在性和稳定性。具体来说，我们证明了当系统参数在某些范围内变动时，存在一个不动点的周期解分支被极限环解所取代，而这个极限环解是稳定的。同时，我们还证明了这个极限环解的存在范围是连续的，并给出了一个明确的界限。最后，我们通过一个具体的例子说明了理论结果的可行性。关键词：等变哈密顿系统；极限环分支；KAM 理论；分岔理论Abstract:In this paper, we study the limit cycle branch of a class of five-type Z2-equivariant near-Hamiltonian systems. By constructing an appropriate limit cycle shift function，we analyze the existence and stability of the limit cycle branch using KAM theory and bifurcation theory. Specifically, we prove that when the system parameters change within certain ranges, a fixed point periodic branch is replaced by a limit cycle solution, which is stable. At the same time, we also prove that the range of existence of this limit cycle solution is continuous and give a clear boundary. Finally, we illustrate the feasibility of our theoretical results through a specific example.Keywords: equivariant Hamiltonian system; limit cycle branch; KAM theory; bifurcation theory
