Work

On a Degenerating Limit Theorem of DeMarco–Faber

Year: 2024

Type: article

Abstract: One of our aims is to complement the proof of DeMarco–Faber’s degenerating limit theorem for the family of the unique maximal entropy measures parametrized by a punctured open disk associated to a meromorphic family of rational functions on the complex projective line, degenerating at the puncture. This complementation is done by our main result, which rectifies a key computation in their argument. We also establish and use a direct and explicit translation from degenerating complex dynamics into quantized Berkovich dynamics, instead of using DeMarco–Faber’s more conceptual transfer principle between those dynamics.

Source: Publications of the Research Institute for Mathematical Sciences

DOI: 10.4171/prims/60-1-2

Author: Yûsuke Okuyama

Institution: Kyoto Institute of Technology

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: Centre National de la Recherche Scientifique, Japan Society for the Promotion of Science, Institut des Hautes Études Scientifiques, Université Paris-Saclay

Award: Analytic studies of the moduli and irrationally indifferent cycles in higher dimensional complex and non-archimedean dynamics