A tangential displacement theory for locating perturbed saddles and their manifolds

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dc.contributor.authorBalasuriya, S.
dc.date.issued2011
dc.description.abstractThe stable and unstable manifolds associated with a saddle point in two-dimensional non–area-preserving flows under general time-aperiodic perturbations are examined. An improvement to existing geometric Melnikov theory on the normal displacement of these manifolds is presented. A new theory on the previously neglected tangential displacement is developed. Together, these enable locating the perturbed invariant manifolds to leading order. An easily usable Laplace transform expression for the location of the perturbed time-dependent saddle is also obtained. The theory is illustrated with an application to the Duffing equation.
dc.description.statementofresponsibilitySanjeeva Balasuriya
dc.identifier.citationSIAM Journal on Applied Dynamical Systems, 2011; 10(3):1100-1126
dc.identifier.doi10.1137/100814640
dc.identifier.issn1536-0040
dc.identifier.issn1536-0040
dc.identifier.orcidBalasuriya, S. [0000-0002-3261-7940]
dc.identifier.urihttp://hdl.handle.net/2440/88420
dc.language.isoen
dc.publisherSociety for Industrial and Applied Mathematics
dc.rights© 2011 Society for Industrial and Applied Mathematics
dc.source.urihttps://doi.org/10.1137/100814640
dc.subjectHyperbolic trajectory; nonautonomous flows; aperiodic flows; Melnikov function; saddle stagnation point; Duffing equation
dc.titleA tangential displacement theory for locating perturbed saddles and their manifolds
dc.typeJournal article
pubs.publication-statusPublished

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