非自治周期映射高退化分支的分支方程的不变性
Invariance of bifurcation equations for high degeneracy bifurcations of non-autonomous periodic maps
摘要：
研究了具有$p$映射的参数依赖族生成的非自治$p$ -周期差分方程的Arnold分类中的$A_{n}$型分歧.证明了对任意自然数$n$，退化、非退化和开折的条件相对于合成的循环阶是不变的。证明的主要工具是局部拓扑共轭。不变性的结果是必不可少的正确定义的分支$A_{n}$，和低余维分支相关联，使用所有可能的循环组合物的纤维家庭的映射的$p$ -周期差分方程。最后，我们给出了两个实例，$A_{3}$或燕尾分歧发生在周期二差分方程的分歧条件是不变的。
英文摘要：
Bifurcations of the $A_{n}$ type in Arnold's classification, in non-autonomous $p$-periodic difference equations generated by parameter depending families with $p$ maps, are studied. It is proved that the conditions of degeneracy, non-degeneracy and unfolding are invariant relative to cyclic order of compositions for any natural number $n$. The main tool for the proofs is local topological conjugacy. Invariance results are essential to the proper definition of the bifurcations $A_{n}$, and lower codimension bifurcations associated, using all the possible cyclic compositions of the fiber families of maps of the $p$-periodic difference equation. Finally, we present two actual examples of $A_{3}$ or swallowtail bifurcation occurring in period two difference equations for which the bifurcation conditions are invariant.
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