• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.759-769
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• 2006

Let L : $C\;\rightarrow\;C$ be a hyperbolic automorphism. Then the hyperbolic toral automorphism $L_A\;T^2\;\rightarrow\;T^2$, induced by L, is a chaotic map ([2] pg.192). We characterize hyperbolic toral automorphisms by proving the converse of the above statement.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.105-115
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• 2003

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).