非退化周期解族的分支
Bifurcations from nondegenerate families of periodic solutions
摘要：
通过一个非退化的$k$参数化周期解族$K$，我们得到了线性化$K$系统的乘子+1的几何重数等于$k.$的情形。文献中对$K$的渐近稳定周期解分支进行了深入的研究，并根据乘子+1的代数重数是否等于$k$给出了不同的条件（作者：Malkin，Loud，Melnikov，Yagasaki）.在本文中，我们假设后者是未知的。在这种情况下，渐近稳定性不能被理解，但我们证明了关于周期解的唯一性的信息仍然是可用的。此外，我们证明了这类结果的右手边的可微性是不必要的，我们的定理在一种Lipschitz连续下得到了证明。
英文摘要：
By a nondegenerate $k$-parameterized family $K$ of periodic solutions we understand the situation when the geometric multiplicity of the multiplier +1 of the linearized on $K$ system equals to $k.$ Bifurcation of asymptotically stable periodic solutions from $K$ is well studied in the literature and different conditions have been proposeddepending on whether the algebraic multiplicity of +1 is $k$ or not (by Malkin, Loud, Melnikov, Yagasaki). In this paper we assume that the later is unknown. Asymptotic stability can not be understood in this case, but we demonstrate that the information about uniqueness of periodic solutions is still available. Moreover, we show that differentiability of the right hand sides is not necessary for the results of this kind and our theorems are proven under a kind of Lipschitz continuity.
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