Show simple item record

dc.contributor.authorCastelli, R.
dc.contributor.authorLessard, J.-P.
dc.contributor.authorJames, J.D.M.
dc.date.accessioned2016-06-13T13:11:51Z
dc.date.available2016-06-13T13:11:51Z
dc.date.issued2015-12-31
dc.identifier.issn1536-0040
dc.identifier.urihttp://hdl.handle.net/20.500.11824/96
dc.description.abstractWe present an efficient numerical method for computing Fourier-Taylor expansions of (un)stable manifolds associated with hyperbolic periodic orbits. Three features of the method are that (1) we obtain accurate representation of the invariant manifold as well as the dynamics on the manifold, (2) it admits natural a posteriori error analysis, and (3) it does not require numerically integrating the vector field. Our approach is based on the parameterization method for invariant manifolds, and studies a certain partial differential equation which characterizes a chart map of the manifold. The method requires only that some mild nonresonance conditions hold. The novelty of the present work is that we exploit the Floquet normal form in order to efficiently compute the Fourier-Taylor expansion. A number of example computations are given including manifolds in phase space dimension as high as ten and manifolds which are two and three dimensional. We also discuss computations of cycle-to-cycle connecting orbits which exploit these manifolds.
dc.formatapplication/pdf
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectFloquet normal form
dc.subjectNumerical computation
dc.subjectSpectral approximation
dc.subjectStable/unstable manifolds
dc.titleParameterization of Invariant Manifolds for Periodic Orbits I: Efficient Numerics via the Floquet Normal Formen_US
dc.typeinfo:eu-repo/semantics/conferenceObjecten_US
dc.identifier.doi10.1137/140960207
dc.relation.publisherversionhttp://epubs.siam.org/doi/10.1137/140960207
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US
dc.journal.titleSIAM Journal on Applied Dynamical Systemsen_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record

Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España