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Ballistic Orbits and Front Speed Enhancement for ABC Flows, KAM and non-KAM solutions, front speed enhancement

Tyler McMillen California State University at Fullerton Jack Xin University of California, Irvine Yifeng Yu University of California, Irvine Andrej Zlatoš University of Wisconsin, Madison

Dynamical Systems mathscidoc:1608.11002

arXiv, 15, (3), 2016.6
We study the two main types of trajectories of the ABC ow 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 non-integrable 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 nd and analyze ballistic edge orbits. We discuss the relationship of existence of these orbits with questions concerning front propagation in the presence of ows, in particular, the question of linear (i.e., maximal possible) front speed enhancement rate for ABC ows.
Global trajectories, helical motion, spiral orbits, non-integrable ABC ows
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@inproceedings{tyler2016ballistic,
  title={Ballistic Orbits and Front Speed Enhancement for ABC Flows, KAM and non-KAM solutions, front speed enhancement},
  author={Tyler McMillen, Jack Xin, Yifeng Yu, and Andrej Zlatoš},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160821004553706760352},
  booktitle={arXiv},
  volume={15},
  number={3},
  year={2016},
}
Tyler McMillen, Jack Xin, Yifeng Yu, and Andrej Zlatoš. Ballistic Orbits and Front Speed Enhancement for ABC Flows, KAM and non-KAM solutions, front speed enhancement. 2016. Vol. 15. In arXiv. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160821004553706760352.
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