论文标题
对近似HOPF分叉的周期性轨道分支长度的保证估计值
Guaranteed estimates for the length of branches of periodic orbits for equivariant Hopf bifurcation
论文作者
论文摘要
考虑了源于差分系统的HOPF分叉点的周期轨道的连接分支。假设非线性项满足球中的线性估计值的假设，则提供了分支中包含的周期轨道振幅范围的可计算估计值。如果估计是全球的，则分支是无限的。结果是在模棱两可的设置中配制的，在该设置中，系统可以具有以不同对称组为特征的周期性轨道的多个分支。非本地分析基于模棱两可的度方法，该方法使我们能够处理通用和退化的HOPF分叉。例子说明了这一点。
Connected branches of periodic orbits originating at a Hopf bifurcation point of a differential system are considered. A computable estimate for the range of amplitudes of periodic orbits contained in the branch is provided under the assumption that the nonlinear terms satisfy a linear estimate in a ball. If the estimate is global, then the branch is unbounded. The results are formulated in an equivariant setting where the system can have multiple branches of periodic orbits characterized by different groups of symmetries. The non-local analysis is based on the equivariant degree method, which allows us to handle both generic and degenerate Hopf bifurcations. This is illustrated by examples.
