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Fiber Julia sets of polynomial skew products with super-saddle fixed points
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2021-03-16 , DOI: 10.1090/proc/15345 Shizuo Nakane
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2021-03-16 , DOI: 10.1090/proc/15345 Shizuo Nakane
Abstract:If a polynomial skew product on 
has a relation between two saddle fixed points, fiber Julia sets 
behave discontinuously. That is, as the base variable 
tends to a point 
corresponding to a saddle point, the limits of 
strictly 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.
中文翻译：
具有超鞍点固定点的多项式偏态乘积的光纤Julia集
摘要：如果多项式偏积在两个鞍形固定点之间具有关系，则纤维Julia集的行为会不连续。也就是说，由于基本变量趋向于与鞍点相对应的点，因此严格限制为。当地图在这些鞍点处可线性化时，我们已经根据[印第安纳大学学报（自然科学版）]中的Lavaurs地图描述了它们的行为。数学。J.68（2019），pp.35-61]。在本文中，我们考虑了地图在鞍形固定点不可逆的情况。事实证明，Lavaurs映射必须完全为零。结果，Julia光纤集的限制具有非空的内部空间。
更新日期：2021-04-22
has a relation between two saddle fixed points, fiber Julia sets behave discontinuously. That is, as the base variable tends to a point corresponding to a saddle point, the limits of strictly 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. 中文翻译：
具有超鞍点固定点的多项式偏态乘积的光纤Julia集
摘要：如果多项式偏积在两个鞍形固定点之间具有关系，则纤维Julia集的行为会不连续。也就是说，由于基本变量趋向于与鞍点相对应的点，因此严格限制为。当地图在这些鞍点处可线性化时，我们已经根据[印第安纳大学学报（自然科学版）]中的Lavaurs地图描述了它们的行为。数学。J.68（2019），pp.35-61]。在本文中，我们考虑了地图在鞍形固定点不可逆的情况。事实证明，Lavaurs映射必须完全为零。结果，Julia光纤集的限制具有非空的内部空间。
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