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dc.contributor.authorToni, Bourama ( )
dc.date.accessioned2019-11-22T18:04:34Z
dc.date.available2019-11-22T18:04:34Z
dc.date.issued1999-09-20
dc.identifier.citationToni, B. (1999). Higher order branching of periodic orbits from polynomial isochrones. Electronic Journal of Differential Equations, 1999(35), pp. 1-15.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/8880
dc.description.abstractWe discuss the higher order local bifurcations of limit cycles from polynomial isochrones (linearizable centers) when the linearizing transformation is explicitly known and yields a polynomial perturbation one-form. Using a method based on the relative cohomology decomposition of polynomial one-forms complemented with a step reduction process, we give an explicit formula for the overall upper bound of branch points of limit cycles in an arbitrary n degree polynomial perturbation of the linear isochrone, and provide an algorithmic procedure to compute the upper bound at successive orders. We derive a complete analysis of the nonlinear cubic Hamiltonian isochrone and show that at most nine branch points of limit cycles can bifurcate in a cubic polynomial perturbation. Moreover, perturbations with exactly two, three, four, six, and nine local families of limit cycles may be constructed.en_US
dc.formatText
dc.format.extent15 pages
dc.format.medium1 file (.pdf)
dc.language.isoen_USen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 1999, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectLimit cyclesen_US
dc.subjectIsochronesen_US
dc.subjectPerturbationsen_US
dc.subjectCohomology decompositionen_US
dc.titleHigher Order Branching of Periodic Orbits from Polynomial Isochronesen_US
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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