REGULAR BRANCHED COVERING SPACES AND CHAOTIC MAPS ON THE RIEMANN SPHERE

- Journal title : Communications of the Korean Mathematical Society
- Volume 19, Issue 3, 2004, pp.507-517
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2004.19.3.507

Title & Authors

REGULAR BRANCHED COVERING SPACES AND CHAOTIC MAPS ON THE RIEMANN SPHERE

Lee, Joo-Sung;

Lee, Joo-Sung;

Abstract

Let (2,2,2,2) be ramification indices for the Riemann sphere. It is well known that the regular branched covering map corresponding to this, is the Weierstrass P function. Lattes [7] gives a rational function R(z)= which is chaotic on and is induced by the Weierstrass P function and the linear map L(z) = 2z on complex plane C. It is also known that there exist regular branched covering maps from onto if and only if the ramification indices are (2,2,2,2), (2,4,4), (2,3,6) and (3,3,3), by the Riemann-Hurwitz formula. In this paper we will construct regular branched covering maps corresponding to the ramification indices (2,4,4), (2,3,6) and (3,3,3), as well as chaotic maps induced by these regular branched covering maps.

Keywords

chaotic map;branched covering space;Weierstrass P function;the Riemann sphere;

Language

English

Cited by

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