Julia sets of certain exponential functions

[摘要] We characterize the Julia sets of certain exponential functions. We show that the Julia sets J(F-lambdan) of F-lambdan(z) = lambda (n)e(zn) where lambda (n) > 0 is the whole plane C, provided that lim(k-->infinity)F(lambdan)(k) (0) = infinity. In particular this is rrna when lambda (n) are real number; such that lambda (n) > (1/ne)(1/n). On the other hand, if 0 < (n) < (1/ne)(1/n), then J(F-n) is nowhere dense in C and is the complement of the basin of attraction of the unique real attractive fixed point of F-lambdan. We then prove similar results for the functions [GRAPHICS] where lambda (i) epsilon C - {0}, 1 less than or equal to i less than or equal to n + 1, a(j) > 1, less than or equal to j less than or equal to n, and m, n greater than or equal to 1. (C) 2000 Academic Press.

[发布日期] 2000-10-15

[关键词] Julia sets;exponential functions