论文标题
重新审视二次家庭的熵单调性和超级巨星周期
Entropy monotonicity and superstable cycles for the quadratic family revisited
论文作者
论文摘要
本文的主要结果是使用对二次地图家族的拓扑熵的单调性进行的证明，有时称为Milnor的单调性猜想。相反，现有的证据以一种或另一种方式依赖于复杂分析。我们的证明是基于作者和合作者先前开发的工具和算法来计算多模式图的拓扑熵。具体而言，我们使用地图的横向相交数量与所谓的临界线路迭代。该方法在技术上很简单且几何。由于这两个主题都是密切相关的，因此还使用了相同的方法来简要重新审视二次图的超级循环。
The main result of this paper is a proof using real analysis of the monotonicity of the topological entropy for the family of quadratic maps, sometimes called Milnor's Monotonicity Conjecture. In contrast, the existing proofs rely in one way or another on complex analysis. Our proof is based on tools and algorithms previously developed by the authors and collaborators to compute the topological entropy of multimodal maps. Specifically, we use the number of transverse intersections of the map iterates with the so-called critical line. The approach is technically simple and geometrical. The same approach is also used to briefly revisit the superstable cycles of the quadratic maps, since both topics are closely related.
