Monotonicity of entropy for real multimodal maps
Monotonicity of entropy for real multimodal maps
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DOI：
10.1090/s0894-0347-2014-00795-5
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发表时间：
2009-05
影响因子：
3.9
通讯作者：
H. Bruin;S. Strien
中科院分区：
文献类型：
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作者：
H. Bruin;S. Strien
Milnor在[16]中提出单调性猜想，即拓扑熵为常数的真实的多峰多项式区间映射族中的参数集是连通的。Milnor & Thurston [17]证明了二次映射的猜想，Milnor & Tresser证明了三次映射的猜想，参见[18]和[5]。在本文中，我们将证明一般情况。
In [16], Milnor posed the Monotonicity Conjecture that the set of parameters within a family of real multimodal polynomial interval maps, for which the topological entropy is constant, is connected. This conjecture was proved for quadratic by Milnor & Thurston [17] and for cubic maps by Milnor & Tresser, see [18] and also [5]. In this paper we will prove the general case.