## Abstract

We consider the monotone twist map f̄ on (ℝ/ℤ) × ℝ, its lift f on ℝ^{2} and its associated variational principle h: ℝ^{2} → through its generating function. By working with the variational principle h, we first show that for an adjacent minimal chain {(u^{k}, v^{k})}_{k=s}^{t} of fixed points of f, if there exists a barrier B_{k} for each adjacent minimal pair u^{k} < u^{k+1}, s ≤ k ≤ t - 1, then there exists a heteroclinic orbit between (u^{s}, v^{s}) and (u^{t}, v^{t}), 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 Λ^{m} ⊂ (ℝ/ℤ) × ℝ such that the shift map of the n-symbol space is a factor of f̄^{m}Λ^{m}, where n is the total number of the globally minimal fixed points of f̄.

Original language | English (US) |
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Pages (from-to) | 69-95 |

Number of pages | 27 |

Journal | Discrete and Continuous Dynamical Systems |

Volume | 9 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2003 |

## Keywords

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

## ASJC Scopus subject areas

- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics