SMALE HORSESHOE MAP VIA TERNARY NUMBERS

Abstract

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