Ballistic orbits and front speed enhancement for ABC flows

Tyler McMillen Jack Xin Yifeng Yu Andrej Zlatos

Classical Analysis and ODEs mathscidoc:1912.43885

SIAM Journal on Applied Dynamical Systems, 15, (3), 1753-1782, 2016.9
We study the two main types of trajectories of the ABC flow in the near-integrable regime: spiral orbits and edge orbits. The former are helical orbits which are perturbations of similar orbits that exist in the integrable regime, while the latter exist only in the nonintegrable regime. We prove existence of ballistic (i.e., linearly growing) spiral orbits by using the contraction mapping principle in the Hamiltonian formulation, and we also find and analyze ballistic edge orbits. We discuss the relationship of existence of these orbits with questions concerning front propagation in the presence of flows, in particular the question of linear (i.e., maximal possible) front speed enhancement rate for ABC flows.
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@inproceedings{tyler2016ballistic,
  title={Ballistic orbits and front speed enhancement for ABC flows},
  author={Tyler McMillen, Jack Xin, Yifeng Yu, and Andrej Zlatos},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210436030802449},
  booktitle={SIAM Journal on Applied Dynamical Systems},
  volume={15},
  number={3},
  pages={1753-1782},
  year={2016},
}
Tyler McMillen, Jack Xin, Yifeng Yu, and Andrej Zlatos. Ballistic orbits and front speed enhancement for ABC flows. 2016. Vol. 15. In SIAM Journal on Applied Dynamical Systems. pp.1753-1782. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210436030802449.
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