Work

Cubic rational maps with escaping critical points, Part Ⅱ: Classification of Julia sets in the case of a parabolic fixed point

Year: 2025

Type: article

Abstract: Julia sets of bi-critical rational maps are either connected or a Cantor set. This Julia set dichotomy has been extended to any cubic rational map with all critical points escaping to an attracting fixed point. In this paper, we classified the Julia set of an arbitrary cubic rational map with all critical points escaping to a parabolic fixed point. We proved a Julia set trichotomy (connected, Cantor set, semi-Cantor set) for such cubic rational maps when the multiplier at the parabolic fixed point is 1.

Source: Discrete and Continuous Dynamical Systems

DOI: 10.3934/dcds.2025062

Authors: Jun Hu, Arkady Etkin

Institutions: City University of New York, Brooklyn College, The Graduate Center, CUNY

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: City University of New York

OpenAlex ID: W4410241076

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Cites: 11

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Related to: 10