From Morse-Smale to all knots and links
Dynamical Systems
2016-09-07 v1 Geometric Topology
Abstract
We analyse the topological (knot-theoretic) features of a certain codimension-one bifurcation of a partially hyperbolic fixed point in a flow on originally described by Shil'nikov. By modifying how the invariant manifolds wrap around themselves, or ``pleat,'' we may apply the theory of templates, or branched two-manifolds, to capture the topology of the flow. This analysis yields a class of flows which bifurcate from a Morse-Smale flow to a Smale flow containing periodic orbits of all knot and link types.
Keywords
Cite
@article{arxiv.math/9708208,
title = {From Morse-Smale to all knots and links},
author = {Robert Ghrist and Todd Young},
journal= {arXiv preprint arXiv:math/9708208},
year = {2016}
}