抛物有理映射的Birkhoff平均的热力学形式与多重分形分析
Thermodynamic formalism and multifractal analysis of Birkhoff averages for parabolic rational maps
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中文总结 AI 辅助
本文针对抛物有理映射，利用热力学形式建立条件变分原理，证明Birkhoff谱的实解析性与严格单调性及最优测度的存在唯一性。
中文摘要 AI 辅助
本文研究了抛物有理映射的Birkhoff平均的多重分形分析。我们建立了一个条件变分原理，并在某一区域上证明了Birkhoff谱的实解析性和严格单调性，以及达到条件变分原理中上确界的测度的存在唯一性。为此，我们在合适的定义域上证明了扩张平衡测度的存在唯一性以及压力函数的实解析性。对于抛物系统，我们采用热力学形式的方法为建立条件变分原理和研究Birkhoff谱的精细性质（包括其实解析性、严格单调性以及在某一区域上达到上确界的测度的存在唯一性）提供了一个统一框架。
英文摘要
In this paper, we study the multifractal analysis of Birkhoff averages for parabolic rational maps. We establish a conditional variational principle and prove the real analyticity and strict monotonicity of the Birkhoff spectrum, as well as the existence and uniqueness of the measure attaining the supremum in the conditional variational principle, on a certain region. To this end, we prove the existence and uniqueness of an expanding equilibrium measure and the real analyticity of the pressure function on a suitable domain. For parabolic systems, our approach using thermodynamic formalism provides a unified framework for establishing the conditional variational principle and investigating finer properties of the Birkhoff spectrum, including its real analyticity, strict monotonicity, and the existence and uniqueness of a measure attaining the supremum on a certain region.
发表机构
- Graduate School of Mathematics, Nagoya University（名古屋大学大学院数学研究院）
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