Lyapunov Spectrum of Asymptotically Sub-additive Potentials
Lyapunov Spectrum of Asymptotically Sub-additive Potentials
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DOI：
10.1007/s00220-010-1031-x
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发表时间：
2010-07-01
影响因子：
2.4
通讯作者：
Huang, Wen
中科院分区：
文献类型：
--
作者：
Feng, De-Jun;Huang, Wen
对于一般渐近次可加势(分别为.一般拓扑动力系统的李雅普诺夫指数水平集的拓扑熵、测度论的拓扑熵和拓扑压之间的一些变分关系。我们的大部分结果是在没有假设存在唯一的平衡测度或压力函数的可微性的情况下得到的。构造了一些例子来说明在次可加情形和在熵映射不是上半连续的情况下多重分形行为的不规则性和复杂性。
For general asymptotically sub-additive potentials (resp. asymptotically additive potentials) on general topological dynamical systems, we establish some variational relations between the topological entropy of the level sets of Lyapunov exponents, measure-theoretic entropies and topological pressures in this general situation. Most of our results are obtained without the assumption of the existence of unique equilibrium measures or the differentiability of pressure functions. Some examples are constructed to illustrate the irregularity and the complexity of multifractal behaviors in the sub-additive case and in the case that the entropy map is not upper-semi continuous.