Journal of applied mathematics & informatics
- Volume 22 Issue 1_2
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- Pages.339-350
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- 2006
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- 2734-1194(pISSN)
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- 2234-8417(eISSN)
LOCATING AND COUNTING BIFURCATION POINTS OF SATELLITE COMPONENTS FROM THE MAIN COMPONENT IN THE DEGREE-n BIFURCATION SET
- Geum Young-Hee (Department of Applied Mathematics, Dankook University) ;
- Kim Young-Ik (Department of Applied Mathematics, Dankook University)
- Published : 2006.09.01
Abstract
The bifurcation point where a satellite component buds from another component is characterized by the existence of the common tangent line between the two osculating components appearing in the degree-n bifurcation set. We investigate the existence, location and number of bifurcation points for satellite components budding from the main component in the degree-n bifurcation set as well as a parametric boundary equation of the main component of the degree-n bifurcation set. Cusp points are also located on the boundary of the main component. Typical degree-n bifurcation sets and their components are illustrated with some computational results.
Keywords
- Bifurcation point;
- cusp point;
- degree-n bifurcation set;
- main component;
- Mandelbrot set;
- root point;
- satellite component