THE CREATION OF HORSESHOES

We present results which describe constraints on the order in which periodic orbits can appear when a horseshoe is created. We associate two rational numbers q(R) and r(R) to each periodic orbit R of the horseshoe, which have the property that if r(R) < q(S) then the orbit R must appear after the orbit S; while if r (S) < r (R) and q (R) < q (S) then either orbit can appear before the other. The time required to compute these quantities is bounded by a linear function of the period of R. We also present an algorithm for determining the rotation interval of a horseshoe orbit, and describe techniques for obtaining lower bounds on the topological entropy of a horseshoe orbit.