Journal article

Publication year: 2001

Pages: 347-372

Journal: Pacific Journal of Mathematics

Volume number: 198

Issue number: 2

ISSN: 0030-8730

Open access status: Bronze

Publisher: Mathematical Sciences Publishers (MSP)

Abstract: 
For a sequence (c(n)) of complex numbers we consider the quadratic polynomials fc(n) (z) : = z(2) + c(n) and the sequence (F-n) of iterates F-n : = f(cn)circle...circlef(c1). The Fatou set F-(cn) is by definition the set of all z is an element of (C) over cap such that (F-n) is normal in some neighbourhood of z, while the complement of F-(cn) is called the Julia set J((cn)). The aim of this article is to study geometric properties, Lebesgue measure and Hausdorff dimension of the Julia set J((cn)) provided that the sequence (c(n)) is bounded.

Harvard Citation style: Brück, R. (2001) Geometric properties of Julia sets of the composition of polynomials of the form z²+c_n, Pacific Journal of Mathematics, 198(2), pp. 347-372

APA Citation style: Brück, R. (2001). Geometric properties of Julia sets of the composition of polynomials of the form z²+c_n. Pacific Journal of Mathematics. 198(2), 347-372.