On the Dynamics of Rational Maps with Two Free Critical Points

2016/05/28 by HyeGyong Jang, Jang, HyeGyong, Norbert Steinmetz +1
Mathematics · Physics and Astronomy · #37F10 #37F15 #37F45 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1605.08903

openalex publication_date 2016/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we discuss the dynamical structure of the rational family (f_t) given by f_t(z)=tz^m((1-z)/(1+z))ⁿ (m≥ 2,~t≠ 0). Each map f_t has two super-attracting immediate basins and two free critical points. We prove that for 0

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