同宿切附近单峰映射扰动的极大吸引子
Maximal attractors for perturbations of unimodal maps near a homoclinic tangency
AI总结：
本文证明单峰映射族的小平面扰动在同宿切附近参数处存在极大吸引子，该结果适用于具特定双曲性质的一般单峰映射，推广了相关学者针对类Hénon族等的已有结果。
AI中文摘要：
我们证明，单峰映射族的小平面扰动在其中一个不动点的同宿切附近参数处，具有极大吸引子（等于其捕获区域迭代的交集）。该结果适用于具有特定双曲性质的一般单峰映射，因此考虑的可允许族包括类Hénon族、类Lozi族或边界碰撞标准形的扰动。因此，我们的结果推广了Viana关于类Hénon族、以及Glendinning和Simpson关于边界碰撞标准形的结果。
英文摘要：
We show that small planar perturbations of families of unimodal maps have maximal (equal to the intersection of the iterates of their trapping region) attractors at parameters near homoclinic tangency of one of the fixed points. The results hold for general unimodal maps exhibiting certain hyperbolic properties. Hence, admissible families considered include Hénon-like families, Lozi-like families, or perturbations of border collision normal forms. Therefore, our results generalize results of Viana in the case of Hénon-like families and Glendinning and Simpson in the case of border collision normal forms.
