2000 character limit reached
On The Dynamics Of The Rational Family $\mathbf{f_t(z)=-\frac{t}{4}\frac{(z^{2}-2)^{2}}{z^{2}-1}}$ (1102.3401v3)
Published 16 Feb 2011 in math.DS and math.CV
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 $\ds f_t(z)=-\frac{t}{4}\frac{(z{2}-2){2}}{z{2}-1}$ with free critical orbit $\pm\sqrt{2}\xrightarrow{(2)}0\xrightarrow{(4)}t\xrightarrow{(1)}...$. 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 Sierpi\'nski curve.