Abstract
Consider the two-dimensional area-preserving map which satisfies the condition that the Smale horseshoe exists at a ≥ ac > 0. In the horseshoe, every periodic orbit is uniquely coded by two symbols 0 and 1. As a result, the symbol sequence s represented by 0 and 1 is determined. For the periodic orbit, the symbol sequence s is the repetition of a finite number of symbols named the code. Suppose that the mother periodic orbit M undergoes the period-doubling bifurcation. Then, the first generation of daughter periodic orbit D1 appears from M. The n (≥ 1)-th generation of daughter periodic orbit Dn is also defined. Let P0 be the code for M and Pn be the code for Dn (n ≥ 1). Our purpose is to derive the coding rule to determine Pn from the given P0. The coding rules for the restricted symmetric periodic orbits are derived.
