Hurder-Rechtman_ETDS2017.pdf (3.65 MB)
Aperiodicity at the Boundary of Chaos
journal contribution
posted on 2019-08-21, 00:00 authored by Steven Hurder, Ana RechtmanWe 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.
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Citation
Hurder, S., & Rechtman, A. (2018). Aperiodicity at the Boundary of Chaos. Ergodic Theory and Dynamical Systems, 38(7), 2683-2728. doi:10.1017/etds.2016.144Publisher
American Mathematical SocietyLanguage
- en
issn
0143-3857Issue date
2017-04-01Usage metrics
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