论文标题
Hölder电位压力的刚度和通过它们的分析功能的拟合
Rigidity of pressures of Hölder potentials and the fitting of analytic functions via them
论文作者
论文摘要
这项工作的第一部分致力于研究有限类型的移位空间上Hölder电位的高压功能的较高差异。通过描述相关随机过程的中心极限定理的压力函数的差异，我们发现了各种阶的差分之间的一些刚性关系。刚性在全球范围内通过Hölder电位的压力功能施加了构成候选凸的分析功能的障碍，这回答了Kucherenko-quas的问题。在工作的第二部分中，我们考虑通过局部恒定电势的压力函数拟合候选分析细菌。我们证明，只要符号集的数量足够大，就可以通过某些局部电位的压力来实现所有1级候选细菌。通过在工作中获得的局部恒定电位的压力，在拟合2级细菌时也有一些结果。
The first part of this work is devoted to the study of higher differentials of pressure functions of Hölder potentials on shift spaces of finite type. By describing the differentials of pressure functions via the Central Limit Theorem for the associated random processes, we discover some rigid relationships between differentials of various orders. The rigidity imposes obstructions on fitting candidate convex analytic functions by pressure functions of Hölder potentials globally, which answers a question of Kucherenko-Quas. In the second part of the work we consider fitting candidate analytic germs by pressure functions of locally constant potentials. We prove that all 1-level candidate germs can be realised by pressures of some locally constant potentials, as long as number of the symbolic set is large enough. There are also some results on fitting 2-level germs by pressures of locally constant potentials obtained in the work.
