A cubic polynomial with a marked fixed point 0 is called an IS-capture polynomial if it has a Siegel disk D around 0 and if D contains an eventual image of a critical point. We show that any IS-capture polynomial is on the boundary of a unique bounded hyperbolic component of the polynomial parameter space determined by the rational lamination of the map and relate IS-capture polynomials to the cubic principal hyperbolic domain and its closure.

中文翻译：

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Siegel 捕获多项式在参数空间中的位置

带有标记不动点 0 的三次多项式称为IS -捕获多项式，如果它的 Siegel 圆盘D大约为 0，并且D包含临界点的最终图像。我们表明，任何 IS 捕获多项式都位于由映射的有理分层确定的多项式参数空间的唯一有界双曲分量的边界上，并将 IS 捕获多项式与三次主双曲域及其闭包相关联。