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1993 Dynamics of certain nonconformal degree-two maps of the plane
Ben Bielefeld, Scott Sutherland, Folkert Tangerman, J. J. P. Veerman
Experiment. Math. 2(4): 281-300 (1993).


We consider the rational maps given by $z \mapsto |z|^{2\alpha-2}z^2+c$, for $z$ and $c$ complex and $\alpha > {1\over 2}$ fixed and real. The case $\alpha=1$ corresponds to quadratic polynomials: some of the well-known results for this conformal case still hold for $\alpha$ near $1$, while others break down. Among the differences between the two cases are the possibility, for $\alpha\ne1$, of periodic attractors that do not attract the critical point, and the fact that for $\alpha >1$ the Julia set is smooth for an open set of values of $c$. Numerical evidence suggests that the analogue of the Mandelbrot set for this family is connected, but not locally connected if $\alpha \ne 1$.


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Ben Bielefeld. Scott Sutherland. Folkert Tangerman. J. J. P. Veerman. "Dynamics of certain nonconformal degree-two maps of the plane." Experiment. Math. 2 (4) 281 - 300, 1993.


Published: 1993
First available in Project Euclid: 24 March 2003

zbMATH: 0816.30015
MathSciNet: MR1281476

Primary: 58F23
Secondary: 30D05

Rights: Copyright © 1993 A K Peters, Ltd.

Vol.2 • No. 4 • 1993
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