Shadowing orbits of ordinary differential equations on invariant submanifolds

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9 Scopus citations


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 ℝm 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 languageEnglish (US)
Pages (from-to)203-216
Number of pages14
JournalTransactions of the American Mathematical Society
Issue number1
StatePublished - 1997


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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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