SMALE HORSESHOE MAP VIA TERNARY NUMBERS

Smale's horseshoe map has become a standard example in the study of discrete dynamical systems. Smale's horseshoe map occurs in a wide range of physical problems with chaotic dynamics on an invariant set. It's chaotic behavior is usually shown by first conjugating it to the two-sided shift map. The authors give a more elementary treatment of a special, but typical case. The only technical background needed is the Cantor set and its ternary representation.