Heteroclinic orbits and chaotic invariant sets for monotone twist maps

Tifei Qian, Zhihong Xia

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We consider the monotone twist map f̄ on (ℝ/ℤ) × ℝ, its lift f on ℝ2 and its associated variational principle h: ℝ2 → through its generating function. By working with the variational principle h, we first show that for an adjacent minimal chain {(uk, vk)}k=st of fixed points of f, if there exists a barrier Bk for each adjacent minimal pair uk < uk+1, s ≤ k ≤ t - 1, then there exists a heteroclinic orbit between (us, vs) and (ut, vt), then by assuming that there is a barrier for any two neighboring globally minimal critical points and m is sufficiently large, we construct an invariant set Λm ⊂ (ℝ/ℤ) × ℝ such that the shift map of the n-symbol space is a factor of f̄mΛm, where n is the total number of the globally minimal fixed points of f̄.

Original languageEnglish (US)
Pages (from-to)69-95
Number of pages27
JournalDiscrete and Continuous Dynamical Systems
Issue number1
StatePublished - Jan 2003


  • Chaotic invariant sets
  • Hamiltonian dynamics
  • Twist maps
  • Variational method

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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