CHAOTIC HOMEOMORPHISMS OF C INDUCED BY HYPERBOLIC TORAL AUTOMORPHISMS AND BRANCHED COVERINGS OF C

Title & Authors
CHAOTIC HOMEOMORPHISMS OF C INDUCED BY HYPERBOLIC TORAL AUTOMORPHISMS AND BRANCHED COVERINGS OF C
Lee, Joo-Sung;

Abstract
It is well known that there exists a regular branched covering map from T$\small{^2}$ onto $\small{\={C}}$ iff the ramification indices are (2,2,2,2), (2,4,4), (2,3,6) and (3,3,3). In this paper we construct (count-ably many) chaotic homeomorphisms induced by hyperbolic toral automorphism and regular branched covering map corresponding to the ramification indices (2,2,2,2). And we also gave an example which shows that the above construction of a chaotic map is not true in general if the ramification indices is (2,4,4) and also show that there are no chaotic homeomorphisms induced by hyperbolic toral automorphism and regular branched covering map corresponding to the ramification indices (2,3,6) and (3,3,3).
Keywords
branched covering;chaotic map;hyperbolic toral automorphism;Weierstrass P function and the Riemann sphere;
Language
English
Cited by
References
1.
Amer. Math. Monthly, 1992. vol.99. pp.332-334

2.
Functions of One Complex Variable(2nd ed.), 1978.

3.
An Introduction to Chaotic Dynamical Systems, 1987.

4.
Acta Math., 1993. vol.171. pp.263-297

5.
London Math. Soc. Lecture Notes Series, 1973. vol.9.

6.
C. R. Acad. Sci. Paris, 1918. vol.166. pp.26-28

7.
Friedr. Vieweg and Sohn Verlagsgesellschft mbH, 1999.

8.
Pitman Research Notes in Math. Series, 1987. vol.161.

9.
Amer. Math. Monthly, 1997. vol.104. pp.411-414

10.
Translations of Mathematical Monographs;Amer. Math. Soc., 1997. vol.170.