Shadowing orbits of ordinary differential equations on invariant submanifolds

DOI10.1090/S0002-9947-97-01783-2zbMath0866.34010OpenAlexW1587774045MaRDI QIDQ5690971

Brian A. Coomes

Publication date: 9 January 1997

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-97-01783-2

zbMATH Keywords

invariant manifoldsHamiltonian systemsfirst integralsshadowingautonomous ordinary differential equationscomputer generated approximate orbitstime shadowing theorem

Mathematics Subject Classification ID

Error bounds for numerical methods for ordinary differential equations (65L70) Numerical analysis in abstract spaces (65J99)

Related Items (3)

A survey of shadowing methods for numerical solutions of ordinary differential equations ⋮ CHAOS ON HYPERSPACE ⋮ A numerical \(C^{1}\)-shadowing result for retarded functional differential equations

Cites Work

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• Rigorous computational shadowing of orbits of ordinary differential equations
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• Numerical orbits of chaotic processes represent true orbits
• Rigorous verification of trajectories for the computer simulation of dynamical systems
• A Shadowing Lemma Approach to Global Error Analysis for Initial Value ODEs
• Generic Properties of Polynomial Vector Fields at Infinity

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