학술저널
AN ESCAPE CRITERION FOR THE COMPLEX POLYNOMIAL, WITH APPLICATIONS TO THE DEGREE-n BIFURCATION SET
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 16, No. 1
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2003.061 - 8 (8 pages)
- 0
Abstract. Let P c (z) = z n + c be a complex polynomial with an integer n ≥ 2. We derive a criterion that the critical orbit of P c escapes to infinity and investigate its applications to the degree-n bifurcation set. The intersection of the degree-n bifurcation set with the real line as well as with a typical symmetric axis is explicitly written as a function of n. A well-defined escape-time algorithm is also included for the improved construction of the degree-n bifurcation set.
1. Introduction
2. An escape criterion for the complex polynomial
3. Applications and concluding remarks
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