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Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 27, No. 1, pp. 77-88 (2011)
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Computer generated images for quadratic rational maps with a periodic critical point

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Dustin Gage and Daniel Jackson

University of Maine at Farmington

**Abstract:** We describe an algorithm for distinguishing hyperbolic components in the parameter space of quadratic rational maps with a periodic critical point. We then illustrate computer images of the hyperbolic components of the parameter spaces $V_1-V_4$, which were produced using our algorithm. We also resolve the singularities of the projective closure of $V_5$ by blowups, giving an alternative proof that as an algebraic curve, the geometric genus of $V_5$ is 1. This explains why we are unable to produce an image for $V_5$.

**Keywords:** rational map, complex dynamics, plane curve singularities, geometric genus, hyperbolic maps, Mandelbrot set

**Classification (MSC2000):** 37F45; 37F10,14H50

**Full text of the article:**

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© 2011
FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition
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