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Let (2; 2; 2; 2) be rami¯cation indices for the Riemann
sphere. It is well known that the regular branched covering map
corresponding to this, is the Weierstrass P function. Lattµes [7]
gives a rational function R(z) =
z4+1
2 g2z2+ 1
16 g2
2
4z3¡g2z which is chaotic on
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 T2 onto ¹ C if and only if the rami¯cation 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 rami¯cation indices (2; 4; 4), (2; 3; 6) and (3; 3;
3), as well as chaotic maps induced by these regular branched cov-
ering maps.
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참고문헌 (8)
참고문헌 신청
/ 1918 / Sur l'iterationdes substitutions rationalles et les fonctions de Poincare : 26 ~ 28
/ 1951 / On Normal Subgroups with nite Index in F-Groups : 56 ~ 58
/ 1952 / On Fenchel's Conjecture about F-Groups : 61 ~ 65
/ 1971 / The Functions of Mathematical Physics
/ 1987 / An Introduction to Chaotic Dynamical Systems
/ 1951 / On Normal Subgroups with nite Index in F-Groups : 56 ~ 58
/ 1952 / On Fenchel's Conjecture about F-Groups : 61 ~ 65
/ 1971 / The Functions of Mathematical Physics
/ 1987 / An Introduction to Chaotic Dynamical Systems
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