论文标题
线性一阶差异操作员及其Hutchinson-Invariant套装
Linear first order differential operators and their Hutchinson-invariant sets
论文作者
论文摘要
在本文中，我们启动了线性普通差分运算符和复杂动力学之间的新相互关系的研究，我们在最简单的订单运营商$ 1 $的情况下进行了详细讨论。也就是说，假设这样的运算符$ t $具有多项式系数，我们将其解释为一个连续的Hutchinson操作员家族，该家族在线性形式的积极力量上作用。使用$ t $的这种解释，我们介绍了其连续的Hutchinson不变平面子集，并研究了它们的各种属性。特别是，我们证明，对于任何具有非恒定系数的$ t $，都存在一个独特的最小值，其中包含不变的集合$ \ mathrm {m}^t_ t_ {ch} $，并在等于$ \ mathbb {c} $时求解。
In this paper, we initiate the study of a new interrelation between linear ordinary differential operators and complex dynamics which we discuss in details in the simplest case of operators of order $1$. Namely, assuming that such an operator $T$ has polynomial coefficients, we interpret it as a continuous family of Hutchinson operators acting on the space of positive powers of linear forms. Using this interpretation of $T$, we introduce its continuously Hutchinson invariant subsets of the complex plane and investigate a variety of their properties. In particular, we prove that for any $T$ with non-constant coefficients, there exists a unique minimal under inclusion invariant set $\mathrm{M}^T_{CH}$ and find explixitly when it equals $\mathbb{C}$.
