Natural Equilibrium States for Multimodal Maps
Natural Equilibrium States for Multimodal Maps
复制标题
多模态地图的自然平衡状态
DOI：
10.1007/s00220-010-1112-x
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发表时间：
2009
影响因子：
2.4
通讯作者：
M. Todd
中科院分区：
文献类型：
--
作者：
G. Iommi;M. Todd
研究了一类真实的多峰映射的热力学形式。这个类包含但大于Collet-Eckmann。对于这类映射，我们证明了几何势− tlog平衡态的存在性和唯一性|DF|，对于参数t的最大可能区间。我们还研究了压力函数的正则性和凸性，完全刻画了一阶相变。还得到了关于Lebesgue测度的绝对连续不变测度的存在性的结果。
This paper is devoted to the study of the thermodynamic formalism for a class of real multimodal maps. This class contains, but it is larger than, Collet-Eckmann. For a map in this class, we prove existence and uniqueness of equilibrium states for the geometric potentials −t log |Df|, for the largest possible interval of parameters t. We also study the regularity and convexity properties of the pressure function, completely characterising the first order phase transitions. Results concerning the existence of absolutely continuous invariant measures with respect to the Lebesgue measure are also obtained.
DOI：
10.1090/s0002-9947-08-04520-0
发表时间：
2008-01-01
影响因子：
1.3
作者：
Melbourne, Ian;Nicol, Matthew
通讯作者：
Nicol, Matthew