Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 6 min ago
PreprintarXiv licencearXiv

Thermodynamic formalism and multifractal analysis of Birkhoff averages for parabolic rational maps

  • Yuya Arima
Open at sourcePDFDOICite

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.

Related

  1. Optimal rates of uniform convergence for weighted Birkhoff averages via almost all rotations
    Zhicheng Tong, Yong Li
    arXivPreprintarXiv licenceFull textDynamical systemsarXiv
  2. Multifractal scaling of quantum eigenfunctions in the thermodynamic limit
    Jonathan P. Keating, Henrik Ueberschaer
    arXivPreprintCC BY 4.0Full textMathematical physicsarXiv
  3. Thermodynamic Formalism on SRB Measures of Compact Convex Projective manifolds, Geometry and Counting
    Patrick Foulon, Inkang Kim
    arXivPreprintarXiv licenceFull textDynamical systemsarXiv
  4. Thermodynamic formalism for partially hyperbolic endomorphisms with critical set
    Kecheng Li
    arXivPreprintarXiv licenceFull textDynamical systemsarXiv
  5. Thermodynamic formalism for non-compact systems with expansivity and specification
    Vaughn Climenhaga, Daniel J. Thompson, Tianyu Wang
    arXivPreprintarXiv licenceFull textDynamical systemsarXiv

Cite

BibTeXRIS
BibTeX
@misc{arima2026thermodynamic,
  title = {{Thermodynamic formalism and multifractal analysis of Birkhoff averages for parabolic rational maps}},
  author = {Yuya Arima},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20036},
  eprint = {2609.20036},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20036},
}
RIS
TY  - UNPB
TI  - Thermodynamic formalism and multifractal analysis of Birkhoff averages for parabolic rational maps
AU  - Yuya Arima
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.20036
UR  - https://arxiv.org/abs/2609.20036
AB  - 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.
ER  -