Work

Spectrum of the basilica group and the associated real and complex 2D dynamics

Year: 2026

Type: preprint

Abstract: In this paper, we study the iteration over the real and complex loci of a specific rational map, found by Grigorchuk and Zuk. This two dimensional map arises as the renormalization map which yields the density of states measure associated with the iterated monodromy group of the Basilica Julia set. It admits two natural complex currents, and we construct their real analogs and show that they are laminar. Finally, this yields some consequences on the properties of the density of states measures and its support.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.31961

Authors: Bedford, Eric, Grigorchuk, Rostislav, Dang, Nguyen-Bac, Lyubich, Mikhail

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7223709560

Cites:

Cited by:

Related to: 10