论文标题
Bowen方程的渐近解决方案在具有可数状态的移位空间上的扰动电势
Asymptotic solution of Bowen equation for perturbed potentials on shift spaces with countable states
论文作者
论文摘要
我们研究了压力函数方程的渐近解决方案$ s \ mapsto p（sφ（ε，\ cdot）+ψ（ε，\ cdot））$用于扰动电势$φ（ε，\ cdot）$和$ψ（ε，\ cdot）$ chiptsions $φ（ε，\ cdot）$（ε，\ cdot）$在移位空间上定义的。在我们的主要结果中，我们为解决方案提供了足够的条件$ s = s（ε）$ $ p（sφ（ε，\ cdot）+ψ（ε，\ cdot））= 0 $，以使小参数$ε$的$ n $ order rorder渐近扩展。此外，我们还获得了解决方案$ s = s（ε）$膨胀顺序小于扰动电势扩展的顺序的情况。我们的结果可以应用于有关从Bowen公式获得的Hausdorff尺寸的渐近行为的问题：共形图形Markov Systems，Markov Systems，一种无限图的定向系统，具有承包性无穷小型映射映射，以及其他具体示例。
We study the asymptotic solution of the equation of the pressure function $s\mapsto P(sφ(ε,\cdot)+ψ(ε,\cdot))$ for perturbed potentials $φ(ε,\cdot)$ and $ψ(ε,\cdot)$ defined on the shift space with countable state space. In our main result, we give a sufficient condition for the solution $s=s(ε)$ of $P(sφ(ε,\cdot)+ψ(ε,\cdot))=0$ to have the $n$-order asymptotic expansion for the small parameter $ε$. In addition, we also obtain the case where the order of the expansion of the solution $s=s(ε)$ is less than the order of the expansion of the perturbed potentials. Our results can be applied to problems concerning asymptotic behaviors of Hausdorff dimensions obtained from Bowen formula: conformal graph directed Markov systems, an infinite graph directed systems with contractive infinitesimal similitudes mappings, and other concrete examples.
