On the structure of isentropes of real polynomials
On the structure of isentropes of real polynomials
复制标题
DOI：
10.1112/jlms.12207
复制
发表时间：
2019-01
期刊：
影响因子：
--
通讯作者：
O. Kozlovski
中科院分区：
文献类型：
--
作者：
O. Kozlovski
在本文中，我们将修改Milnor-Thurston映射，它将一维映射映射到相同熵的分段线性，并研究其性质。这将允许我们给出真实的多项式的拓扑熵的单调性的简单证明，并且更好地理解一维映射何时可以和不能被相同熵的双曲映射近似。特别是，我们会发现地图的特定组合，不能近似的双曲映射相同的熵。
In this paper, we will modify the Milnor–Thurston map, which maps a one‐dimensional mapping to a piece‐wise linear of the same entropy, and study its properties. This will allow us to give a simple proof of monotonicity of topological entropy for real polynomials and better understand when a one‐dimensional map can and cannot be approximated by hyperbolic maps of the same entropy. In particular, we will find maps of particular combinatorics which cannot be approximated by hyperbolic maps of the same entropy.