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 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 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 |
DOIs | |
State | Published - 1997 |
Keywords
- First integrals
- Hamiltonian systems
- Invariant manifolds
- Ordinary differential equations
- Shadowing
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics