Thermodynamic formalism and multifractal analysis of Birkhoff averages for parabolic rational maps
Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Arima, Yuya
Institution: Nagoya University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: 二次写像族とリャプノフ非正則集合
OpenAlex ID: W7213601454