The essential coexistence phenomenon in Hamiltonian dynamics

Jianyu Chen; Huyi Hu; Yakov Pesin; Ke Zhang

doi:10.1017/etds.2021.13

The essential coexistence phenomenon in Hamiltonian dynamics

Dynamical Systems 2021-07-01 v2

Authors: Jianyu Chen , Huyi Hu , Yakov Pesin , Ke Zhang

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Abstract

We construct an example of a Hamiltonian flow $f^t$ on a $4$ -dimensional smooth manifold $\mathcal{M}$ which after being restricted to an energy surface $\mathcal{M}_e$ demonstrates essential coexistence of regular and chaotic dynamics that is there is an open and dense $f^t$ -invariant subset $U\subset\mathcal{M}_e$ such that the restriction $f^t|U$ has non-zero Lyapunov exponents in all directions (except the direction of the flow) and is a Bernoulli flow while on the boundary $\partial U$ , which has positive volume all Lyapunov exponents of the system are zero.

Keywords

geodesic flow geometric flows holomorphic dynamics

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@article{arxiv.1901.07713,
  title  = {The essential coexistence phenomenon in Hamiltonian dynamics},
  author = {Jianyu Chen and Huyi Hu and Yakov Pesin and Ke Zhang},
  journal= {arXiv preprint arXiv:1901.07713},
  year   = {2021}
}

Comments

Ya. P. was partially supported by NSF grant DMS-1400027. The authors would like to thank Banff International Research Station, where part of the work was done, for their hospitality

The essential coexistence phenomenon in Hamiltonian dynamics

Abstract

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