On the continuation of an invariant torus in a family with rapid oscillations
Issue Date
2000-01-01Author
Chicone, Carmen
Liu, Weishi
Publisher
Society for Industrial and Applied Mathematics
Type
Article
Article Version
Scholarly/refereed, publisher version
Metadata
Show full item recordAbstract
A persistence theorem for attracting invariant tori for systems subjected to rapidly oscillating perturbations is proved. The singular nature of these perturbations prevents the direct application of the standard persistence results for normally hyperbolic invariant manifolds. However, as is illustrated in this paper, the theory of normally hyperbolic invariant manifolds, when combined with an appropriate continuation method, does apply.
Description
This is the published version, also available here: http://dx.doi.org/10.1137/S0036141098338740.
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Citation
Chicone, Carmen & Liu, Weishi. "On the continuation of an invariant torus in a family with rapid oscillations." SIAM J. Math. Anal., 31(2), 386–415. (30 pages). http://dx.doi.org/10.1137/S0036141098338740.
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