Bifurcational Precedences in the Braids of Periodic Orbits of Spiral 3-Shoes in Driven Oscillators

We conjecture the existence of a 3-striped spiral horseshoe under one iterate of the Poincare map that arises in the analysis of a class of driven oscillators. These systems represent escape from a smooth potential well under periodic forcing. We assume topological conjugacy between the flow of the differential equation and an idealized suspension of a spiral 3-shoe, and deduce bifurcational precedences by consideration of intertwining in the braid of periodic orbits. We argue that many significant subharmonic bifurcations observed in such systems can then be understood in terms of the creation of this 3-shoe.