论文标题
一般迭代功能系统的热力学形式主义
Thermodynamic formalism for general iterated function systems with measures
论文作者
论文摘要
本文介绍了具有措施（IFSM）的迭代功能系统的热力学形式主义理论。我们研究了与IFSM相关的传输和Markov操作员的光谱特性。我们介绍了全体措施拓扑熵和IFSM的拓扑压力的变异配方。然后，平衡状态的定义是自然的，我们证明其存在具有任何连续的潜力。在这种情况下，我们显示了仅需要压力功能的gâteaux可不同性的平衡状态的唯一性结果。
This paper introduces a theory of Thermodynamic Formalism for Iterated Function Systems with Measures (IFSm). We study the spectral properties of the Transfer and Markov operators associated to a IFSm. We introduce variational formulations for the topological entropy of holonomic measures and the topological pressure of IFSm given by a potential. A definition of equilibrium state is then natural and we prove its existence for any continuous potential. We show, in this setting, a uniqueness result for the equilibrium state requiring only the Gâteaux differentiability of the pressure functional.
