标题： 轨道图在非自治迭代中 显示英文标题

标题： Orbit Portraits in non-Autonomous Iteration

摘要： 我们将轨道图的定义扩展到非自治迭代的背景下，包括涉及角度集合的组合版本和涉及外部射线的动力版本，其中组合图可以通过具有适当一致有界次数和系数的多项式序列的动力学实现。 我们证明，在多项式序列次数恒定的情况下，出现的图是最终周期性的，这与多项式迭代的经典理论有些相似。 然而，如果允许序列中多项式的次数变化，可以得到具有无理长度互补弧的图，这些图与经典图有根本的不同。 显示英文摘要

摘要： We extend the definition of an orbit portrait to the context of non-autonomous iteration, both for the combinatorial version involving collections of angles and for the dynamic version involving external rays where combinatorial portraits can be realized by the dynamics associated with sequences of polynomials with suitably uniformly bounded degrees and coefficients. We show that, in the case of sequences of polynomials of constant degree, the portraits which arise are eventually periodic which is somewhat similar to the classical theory of polynomial iteration. However, if the degrees of the polynomials in the sequence are allowed to vary, one can obtain portraits with complementary arcs of irrational length which are fundamentally different from the classical ones.