Cyclicity of a class of polynomial nilpotent center singularities
| dc.contributor.author | García, I. A. (Isaac A.) | |
| dc.contributor.author | Shafer, Douglas S. | |
| dc.date.accessioned | 2016-11-08T13:57:41Z | |
| dc.date.issued | 2016-04-01 | |
| dc.date.updated | 2016-11-08T13:57:42Z | |
| dc.description.abstract | In this work we extend techniques based on computational algebra for bounding the cyclicity of nondegenerate centers to nilpotent centers in a natural class of polynomial systems, those of the form $\dot x = y + P_{2m + 1}(x,y)$, $\dot y = Q_{2m + 1}(x,y)$, where $P_{2m+1}$ and $Q_{2m+1}$ are homogeneous polynomials of degree $2m + 1$ in $x$ and $y$. We use the method to obtain an upper bound (which is sharp in this case) on the cyclicity of all centers in the cubic family and all centers in a broad subclass in the quintic family. | |
| dc.description.sponsorship | The first author is partially supported by a MICINN grant number MTM2011-22877 and by a CIRIT grant number 2014 SGR 1204. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.doi | https://doi.org/10.3934/dcds.2016.36.2497 | |
| dc.identifier.idgrec | 023237 | |
| dc.identifier.issn | 1078-0947 | |
| dc.identifier.uri | http://hdl.handle.net/10459.1/58427 | |
| dc.language.iso | eng | |
| dc.publisher | American Institute of Mathematical Sciences | |
| dc.relation | MICINN/PN2008-2011/MTM2011-22877 | |
| dc.relation.isformatof | Versió postprint del document publicat a https://doi.org/10.3934/dcds.2016.36.2497 | |
| dc.relation.ispartof | Discrete and Continuous Dynamical Systems Series A, 2016, vol. 36, núm. 5, p. 2497-2520 | |
| dc.rights | (c) American Institute of Mathematical Sciences, 2016 | |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.subject | Cyclicity | |
| dc.subject | Limit cycle | |
| dc.subject | Nilpotent center | |
| dc.subject.classification | Matemàtica | |
| dc.subject.other | Mathematics | |
| dc.title | Cyclicity of a class of polynomial nilpotent center singularities | |
| dc.type | info:eu-repo/semantics/article | |
| dc.type.version | info:eu-repo/semantics/acceptedVersion |