The Douady-Hubbard landing theorem for periodic external rays is one of the cornerstones of the study of polynomial dynamics. It states that, for a complex polynomial f with bounded postcritical set, every periodic external ray lands at a repelling or parabolic periodic point, and conversely every repelling or parabolic point is the landing point of at least one periodic external ray. We prove an analogue of this theorem for an entire function f with bounded postsingular set. If f has finite order of growth, then it is known that the escaping set I(f) contains certain curves called periodic hairs; we show that every periodic hair lands at a repelling or parabolic periodic point, and conversely every repelling or parabolic periodic point is the landing point of at least one periodic hair. For a postsingularly bounded entire function f of infinite order, such hairs may not exist. Therefore we introduce certain dynamically natural connected subsets of I(f), called dreadlocks. We show that every periodic dreadlock lands at a repelling or parabolic periodic point, and conversely every repelling or parabolic periodic point is the landing point of at least one periodic dreadlock. More generally, we prove that every point of a hyperbolic set is the landing point of a dreadlock.

周期性外部光线的杜阿-哈伯德着陆定理是多项式动力学研究的基石之一。它指出，对于具有后临界集的有界多项式f，每个周期性外部射线都在排斥或抛物线周期点着陆，相反，每个排斥或抛物线点都是至少一个周期性外部射线的着陆点。我们证明了该函数定理的一个有界的奇异集的完整函数f的一个类似物。如果f具有有限的增长阶，则已知逃逸集合I（f）包含某些称为周期性毛发的曲线; 我们表明，每个周期性头发都位于排斥或抛物线的周期性点，相反，每个排斥或抛物线周期性点都是至少一根周期性毛的着陆点。对于无限阶的后置有界整函数f，此类毛可能不存在。因此，我们介绍了I（f）的某些动态自然连接的子集，称为dreadlocks。我们表明，每个周期性辫子都落在一个排斥或抛物线周期点，相反，每个排斥或抛物线周期点都是至少一个周期性辫子的着陆点。更笼统地说，我们证明了双曲集的每个点都是辫子的着陆点。