Journal of the Chungcheong Mathematical Society (충청수학회지)
- Volume 16 Issue 2
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- Pages.43-57
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- 2003
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- 1226-3524(pISSN)
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- 2383-6245(eISSN)
A PARAMETRIC BOUNDARY OF A PERIOD-2 COMPONENT IN THE DEGREE-3 BIFURCATION SET
- Kim, Young Ik (Department of Applied Mathematics Dankook University)
- Received : 2003.10.01
- Published : 2003.12.31
Abstract
The boundary of a typical period-2 component in the degree-3 bifurcation set is formulated by a parametrization of its image which is the unit circle under the multiplier map. Some properties on the geometry of the boundary are investigated including the root point, the cusp and the length as well as the area bounded by the boundary curve. The centroid of the area for the period-2 component was numerically found with high accuracy and compared with its center. An algorithm drawing the boundary curve with Mathematica codes is proposed and its implementation exhibits a good agreement with the analysis presented here.
Keywords
- bifurcation point;
- cusp point;
- degree-n bifurcation set;
- main component;
- multiplier;
- period-k component;
- Mandelbrot set;
- root point