Fiber Julia sets of polynomial skew products with super-saddle fixed points
Fiber Julia sets of polynomial skew products with super-saddle fixed points
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具有超鞍不动点的多项式偏斜积 Fiber Julia 集
DOI：
10.1090/proc/15345
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发表时间：
2021
影响因子：
1
通讯作者：
Shizuo Nakane
中科院分区：
文献类型：
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作者：
Shizuo Nakane
如果上的多项式斜积在两个鞍不动点之间存在关系，则纤维Julia集的行为是不连续的。也就是说，当基变量趋向于一个对应于鞍点的点时，的极限严格包括。当映射在这些鞍点处可线性化时，我们已经在[印第安纳州Univ. Math. J. 68（2019），pp. 35-61]。在这篇文章中，我们考虑的情况下，当地图是不可逆的鞍不动点。结果是Lavaurs映射必须为零。因此，纤维Julia集的极限具有非空的内部。引用
If a polynomial skew product onhas a relation between two saddle fixed points, fiber Julia setsbehave discontinuously. That is, as the base variabletends to a pointcorresponding to a saddle point, the limits ofstrictly include. When the map is linearizable at these saddle points, we have described their behaviors in terms of Lavaurs maps in [Indiana Univ. Math. J. 68 (2019), pp. 35–61]. In this article, we consider the case when the map is not invertible at a saddle fixed point. It turns out that the Lavaurs map must be identically zero. As a result, the limits of fiber Julia sets have non-empty interiors. References