On The Dynamics Of The Rational Family \mathbff_t(z)=-(t)/(4)\frac(z²-2)²z²-1

2011/02/16 by Jang, Hye Gyong, Steinmetz, Norbert
#37F10 #37F15 #37F45 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1102.3401

Abstract

In this paper we discuss the dynamics as well as the structure of the parameter space of the one-parameter family of rational maps \ds f_t(z)=-(t)/(4)\frac(z²-2)²z²-1 with free critical orbit ±√(2)\xrightarrow(2)0\xrightarrow(4)t\xrightarrow(1).... In particular it is shown that for any escape parameter t the boundary of the basin at infinity \A_t is either a Cantor set, a curve with infinitely many complementary components, or else a Jordan curve. In the latter case the Julia set is a Sierpiński curve.

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