In this paper we consider families of holomorphic maps defined on subsets of the complex plane, and show that the technique developed in \cite{LSvS1} to treat unfolding of critical relations can also be used to deal with cases where the critical orbit converges to a hyperbolic attracting or a parabolic periodic orbit. As before this result applies to rather general families of maps, such as polynomial-like mappings, provided some lifting property holds. Our Main Theorem states that either the multiplier of a hyperbolic attracting periodic orbit depends univalently on the parameter and bifurcations at parabolic periodic points are generic, or one has persistency of periodic orbits with a fixed multiplier.

中文翻译：

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双曲线和抛物线图设置中的横向性

在本文中，我们考虑定义在复平面子集上的全纯映射族，并表明 \cite{LSvS1} 中开发的处理临界关系展开的技术也可用于处理临界轨道收敛到双曲线吸引或抛物线周期轨道。和以前一样，这个结果适用于相当一般的映射族，例如多项式类映射，前提是某些提升属性成立。我们的主定理指出，要么双曲线吸引周期轨道的乘数单价取决于参数且抛物线周期点的分岔是通用的，要么具有固定乘数的周期轨道的持久性。