Shadowing orbits of ordinary differential equations on invariant submanifolds

Author:
Brian A. Coomes

Journal:
Trans. Amer. Math. Soc. **349** (1997), 203-216

MSC (1991):
Primary 34A50; Secondary 65L70

DOI:
https://doi.org/10.1090/S0002-9947-97-01783-2

MathSciNet review:
1390974

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Abstract | References | Similar Articles | Additional Information

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 mapping phase space into with the property that for a particular regular value of the submanifold is invariant under the flow. The main theorem gives a condition which implies that an approximate solution lying close to is uniformly close to a true solution lying in . Applications of this theorem to computer generated approximate orbits are discussed.

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Additional Information

**Brian A. Coomes**

Affiliation:
Department of Mathematics and Computer Science, University of Miami, Coral Gables, Florida 33124

Email:
coomes@math.miami.edu

DOI:
https://doi.org/10.1090/S0002-9947-97-01783-2

Keywords:
Ordinary differential equations,
shadowing,
Hamiltonian systems,
first integrals,
invariant manifolds

Received by editor(s):
May 17, 1995

Article copyright:
© Copyright 1997
American Mathematical Society