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http://dx.doi.org/10.4134/CKMS.2004.19.3.507

REGULAR BRANCHED COVERING SPACES AND CHAOTIC MAPS ON THE RIEMANN SPHERE  

Lee, Joo-Sung (Department of Mathematics Dongguk University)
Publication Information
Communications of the Korean Mathematical Society / v.19, no.3, 2004 , pp. 507-517 More about this Journal
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)= ${\frac{z^4+{\frac{1}{2}}g2^{z}^2+{\frac{1}{16}}g{\frac{2}{2}}$ which is chaotic on ${\bar{C}}$ 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 $T^2$ onto ${\bar{C}}$ 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;
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  • Reference
1 /
[ J. Milnor ] / Dynamics in One Complex Variable
2 On Normal Subgroups with finite Index in F-Groups /
[ S. Bundgaard;J. Nielsen ] / Math. Tidsskrift
3 /
[ R. Devaney ] / An Introduction to Chaotic Dynamical Systems
4 A proof of Thurston's Topological Characterization of Rational Functions /
[ A. Douady;J. H. Hubbard ] / Acta Math.   DOI
5 Elliptic Functions and Elliptic Curves /
[ P. Du Val ] / London Math. Soc. Lecture Notes Series 9
6 On Fenchel's Conjecture about F-Groups /
[ R. Fox ] / Math. Tidsskrift
7 /
[ H. Hochstadt ] / The Functions of Mathematical Physics
8 Sur l'iterationdes substitutions rationalles et les fonctions de Poincare /
[ S. Lattes ] / CR Acad. Sci. Paris
9 Branched Coverings and Algebraic Functions /
[ M. Namba ] / Pitman Research Notes in Math. Series 161
10 Elliptic Functions and Elliptic Integrals /
[ V. Prasolov;Y. Solovyev ] / Transl. Math. Monogr.