# THE EXTENDED REAL LINE AS A JULIA SET

• AKBARI, MONIREH ;
• RABII, MARYAM
• Published : 2015.07.31
• 36 7

#### 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

#### References

1. A. F. Beardon, Iteration of Rational Functions, Cambridge, 1991.
2. R. Devaney, An Introduction to Chaotic Dynamical Systems, 2nd. ed., Addison-Wesley, 1989.
3. J. Milnor, Pasting together Julia sets: A worked out example of mating, Experiment. Math. 13 (2004), no. 1, 55-92. https://doi.org/10.1080/10586458.2004.10504523
4. J. Milnor, Dynamics in One Complex Variable, 3rd. ed., Princeton University Press, 2006.