Aperiodicity at the Boundary of Chaos

We consider the dynamical properties of C∞-variations of the flow on an aperiodic Kuperberg plug K. Our main result is that there exists a smooth 1-parameter family of plugs K for ∈ (−a, a) and a < 1, such that: (1) The plug K0 = K is a generic Kuperberg plug; (2) For < 0, the flow in the plug K has two periodic orbits that bound an invariant cylinder, all other orbits of the flow are wandering, and the flow has topological entropy zero; (3) For > 0, the flow in the plug K has positive topological entropy, and an abundance of periodic orbits.