Monotonicity of entropy for real quadratic rational maps
Monotonicity of entropy for real quadratic rational maps
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DOI：
10.1088/1361-6544/ac15aa
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发表时间：
2019-01
期刊：
影响因子：
1.7
通讯作者：
Khashayar Filom
中科院分区：
文献类型：
--
作者：
Khashayar Filom
研究了真实的圆R ∞}上真实的二次有理映射熵的单调性，基于模空间M2（R）的单调、覆盖、单峰和双峰区域的自然划分.利用类多项式映射理论，证明了真实的熵函数hR的水平集在M2（R）的（−+−）-双峰区域和单峰区域的一部分中是连通的.基于数值证据，我们推测单调性在单峰区域中保持，但在（+−+）-双峰映射区域中不成立。
The monotonicity of entropy is investigated for real quadratic rational maps on the real circle R∪{∞} based on the natural partition of the corresponding moduli space M2(R) into its monotonic, covering, unimodal and bimodal regions. Utilizing the theory of polynomial-like mappings, we prove that the level sets of the real entropy function hR are connected in the (−+−)-bimodal region and a portion of the unimodal region in M2(R) . Based on the numerical evidence, we conjecture that the monotonicity holds throughout the unimodal region, but we conjecture that it fails in the region of (+−+)-bimodal maps.