Knotted Periodic Orbits in Suspensions of Smale ' s Horseshoe : Torus Knots and Bifurcation Sequences

@inproceedings{HolmesKnottedPO,
  title={Knotted Periodic Orbits in Suspensions of Smale ' s Horseshoe : Torus Knots and Bifurcation Sequences},
  author={Philip Holmes}
}
We construct a suspension of SMALE'S horseshoe diffeomorphism of the two-dimensional disc as a flow in an orientable three manifold. Such a suspension is natural in the sense that it occurs frequently in periodically forced nonlinear oscillators such as the Duffing equation. From this suspension we construct a knot-hblder or t empla te -a branched two-manifold with a semiflow--in such a way that the periodic orbits are isotopic to those in the full three-dimensional flow. We discuss some of the… CONTINUE READING