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From Morse-Smale to all knots and links

Robert Ghrist·Todd Young
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Abstract

We analyse the topological (knot-theoretic) features of a certain codimension-one bifurcation of a partially hyperbolic fixed point in a flow on $\real^3$ 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.

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Robert Ghrist, Todd Young. 1997-08-22. From Morse-Smale to all knots and links. https://doi.org/10.1088/0951-7715%2F11%2F4%2F021

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