The extended real line as a Julia set

Monireh Akbari; Maryam Rabii

doi:10.4134/BKMS.2015.52.4.1107

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Bull. Korean Math. Soc. 2015; 52(4): 1107-1112

Printed July 31, 2015

https://doi.org/10.4134/BKMS.2015.52.4.1107

The extended real line as a Julia set

Monireh Akbari and Maryam Rabii

Shahid Rajaee Teacher Training University, Alzahra University

Abstract

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Abstract

A recursive family $ \{F_n\} $ of holomorphic functions on the Riemann sphere is defined and some elementary properties of this family is described. Then the Julia set of $ F_n $ is computed. Finally this family as a real recursive family is studied and it is shown that $ F_n $ is chaotic on a specific subset of $ \mathbb{R} $.

Keywords: Julia set, recursive relation, conjugacy, rational function

MSC numbers: 37F50