Rotating periodic solutions in complete degeneracy
Rotating periodic solutions in complete degeneracy
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DOI：
10.1016/j.aml.2022.107945
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发表时间：
2022-01
期刊：
影响因子：
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通讯作者：
Ying Guo;Xue Yang
中科院分区：
文献类型：
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作者：
Ying Guo;Xue Yang
在这篇论文中，我们关注r2n中一类摄动系统上q0 -旋转周期解的存在性。该类旋转周期解的形式为X (t+ t) = q0 X (t),∀t∈R with t > 0，以及q0是一个正交矩阵。所考虑的系统是线性的，但完全简并，换句话说，完全共振。总的来说，解决这个问题是相当困难的。我们建立了q0旋转周期解在小扰动下的持久性结果。我们的横截性条件是基于拓扑度的，但在实际应用中很容易验证。
In the present paper, we are concerned with the existence of Q 0-rotating periodic solutions on a class of perturbed systems in R 2 n. This type of rotating periodic solutions has the form of X (t+ T)= Q 0 X (t),∀ t∈ R with T> 0 and Q 0 an orthogonal matrix. The systems under consideration are linear but completely degenerate, in another word, completely resonant. In general it is quite difficult to the situation. We establish a persistence result about Q 0-rotating periodic solutions undergoing small perturbations. Our transversality condition is based on the topological degree, but easily verifiable in applications.