The essential coexistence phenomenon in Hamiltonian dynamics

Jianyu Chen, Huyi Hu, Yakov Pesin, K. E. Zhang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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

Original languageEnglish (US)
Pages (from-to)592-613
Number of pages22
JournalErgodic Theory and Dynamical Systems
Issue number2
StatePublished - Feb 8 2022

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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