### Abstract

A finite time shadowing theorem for autonomous ordinary differential equations is presented. Under consideration is the case were there exists a twice continuously differentiable function g mapping phase space into ℝ^{m} with the property that for a particular regular value c of g the submanifold g^{-1}(c) is invariant under the flow. The main theorem gives a condition which implies that an approximate solution lying close to g^{-1}(c) is uniformlyclose to a true solution lying in g^{-1}(c). Applications of this theorem to computer generated approximate orbits are discussed.

Original language | English (US) |
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Pages (from-to) | 203-216 |

Number of pages | 14 |

Journal | Transactions of the American Mathematical Society |

Volume | 349 |

Issue number | 1 |

State | Published - Dec 1 1997 |

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### Keywords

- First integrals
- Hamiltonian systems
- Invariant manifolds
- Ordinary differential equations
- Shadowing

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics