Thermodynamic formalism for certain nonhyperbolic maps
Thermodynamic formalism for certain nonhyperbolic maps
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某些非双曲映射的热力学形式主义
DOI：
10.1017/s0143385799141695
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发表时间：
1999
影响因子：
0.9
通讯作者：
M. Yuri
中科院分区：
文献类型：
--
作者：
M. Yuri
对具有可数个原像的非双曲映射建立了一个广义热力学形式。研究了共形测度的存在唯一性以及关于共形测度绝对连续的平衡态的统计性质。我们将看到这样的测度不是吉布斯测度，但满足吉布斯性质的一个版本（弱吉布斯测度）。我们将我们的结果应用到一个单参数族的一维映射和二维非共形映射的数论。它们都承认无差别的周期点。
We establish a generalized thermodynamic formalism for certain nonhyperbolic maps with countably many preimages. We study existence and uniqueness of conformal measures and statistical properties of the equilibrium states absolutely continuous with respect to the conformal measures. We will see that such measures are not Gibbs but satisfy a version of Gibbs property (weak Gibbs measure). We apply our results to a one-parameter family of one-dimensional maps and a two-dimensional nonconformal map related to number theory. Both of them admit indifferent periodic points.