Gage, Dustin and Jackson, Daniel (2011) Computer generated images for quadratic rational maps with a periodic critical point. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 27 (1). pp. 77-88. ISSN 0866-0174
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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 V1 − V4, which were produced using our algorithm. We also resolve the singularities of the projective closure of V5 by blowups, giving an alternative proof that as an algebraic curve, the geometric genus of V5 is 1. This explains why we are unable to produce an image for V5.
| Item Type: | Article |
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| Uncontrolled Keywords: | rational map, complex dynamics, plane curve singularities, geometric genus, hyperbolic maps, Mandelbrot set |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | Zsolt Baráth |
| Date Deposited: | 02 Feb 2024 11:38 |
| Last Modified: | 02 Feb 2024 11:38 |
| URI: | http://real.mtak.hu/id/eprint/187161 |
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