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

Lee, Joo-Sung

• Published : 2003.01.01
• 47 10

#### Abstract

It is well known that there exists a regular branched covering map from T$^2$ onto $\={C}$ 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

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