Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type

dc.contributor.authorZhu, Huaiping
dc.contributor.authorRousseau, Christiane
dc.date.accessioned2007-02-13
dc.date.available2007-02-13
dc.date.issued2002
dc.description.abstractIn this paper we prove finite cyclicity of several of the most generic graphics through a nilpotent point of saddle or elliptic type of codimension 3 inside C . families of planar vector fields. In some cases our results are independent of the exact codimension of the point and depend only on the fact that the nilpotent point has multiplicity 3. By blowing up the family of vector fields, we obtain all the limit periodic sets. We calculate two different types of Dulac maps in the blown-up family and develop a general method to prove that some regular transition maps have a nonzero higher derivative at a point. The finite cyclicity theorems are derived by a generalized derivation–division method introduced by Roussarie.
dc.format.extent796312 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.citationHuaiping Zhu and Christiane Rousseau, Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type. J. Differential Equations 178 (2002), no. 2, 325--436.
dc.identifier.issn0022-0396
dc.identifier.urihttp://hdl.handle.net/10315/913
dc.identifier.urihttps://doi.org/10.1006/jdeq.2001.4017
dc.language.isoen
dc.publisherJournal of Differential Equations (Elsevier Science)
dc.rights© 2002. This manuscript version is made available under the CC-BY-NC-ND 4.0.
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.titleFinite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type
dc.typeArticle

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