The essential coexistence phenomenon in Hamiltonian dynamics

Jianyu Chen, Huyi Hu, Yakov Pesin, Ke Zhang

Research output: Contribution to journalArticlepeer-review

Abstract

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

Original languageEnglish (US)
JournalErgodic Theory and Dynamical Systems
DOIs
StateAccepted/In press - 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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