We investigate boundedness of hyperbolic components in the moduli space of Newton maps. For quartic maps, (i) we prove hyperbolic components possessing two distinct attracting cycles each of period at least two are bounded, and (ii) we characterize the possible points on the boundary at infinity for some other types of hyperbolic components. For general maps, we prove hyperbolic components whose elements have fixed superattracting basins mapping by degree at least three are unbounded.

中文翻译：

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牛顿图双曲分量的有界

我们研究了牛顿映射模空间中双曲分量的有界性。对于四次映射，（i）我们证明双曲分量具有两个不同的吸引周期，每个周期至少有两个有界，并且（ii）我们描述了一些其他类型的双曲分量在无穷远边界上的可能点。对于一般地图，我们证明其元素具有固定超吸引盆地按至少 3 次映射的双曲分量是无界的。