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The Poincaré problem, algebraic integrability and dicritical divisors
dc.contributor.author | Galindo, Carlos | |
dc.contributor.author | Montserrat Delpalillo, Francisco José | |
dc.date.accessioned | 2015-07-01T11:13:38Z | |
dc.date.available | 2015-07-01T11:13:38Z | |
dc.date.issued | 2015-07-01 | |
dc.identifier.issn | 0022-0396 | |
dc.identifier.uri | http://hdl.handle.net/10234/125707 | |
dc.description.abstract | We solve the Poincaré problem for plane foliations with only one dicritical divisor. Moreover, in this case, we give a simple algorithm that decides whether a foliation has a rational first integral and computes it in the affirmative case. We also provide an algorithm to compute a rational first integral of prefixed genus g≠1g≠1 of any type of plane foliation FF. When the number of dicritical divisors dic(F)dic(F) is larger than 2, this algorithm depends on suitable families of invariant curves. When dic(F)=2dic(F)=2, it proves that the degree of the rational first integral can be bounded only in terms of g , the degree of FF and the local analytic type of the dicritical singularities of FF. | ca_CA |
dc.format.extent | 19 p. | ca_CA |
dc.format.mimetype | application/pdf | ca_CA |
dc.language.iso | eng | ca_CA |
dc.relation.isPartOf | Journal of Differential Equations, 2014, 256.11: 3614-3633 | ca_CA |
dc.rights | Copyright © 2014 Elsevier Ltd. All rights reserved | ca_CA |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | * |
dc.subject | Poincaré problem | ca_CA |
dc.subject | algebraic integrability | ca_CA |
dc.title | The Poincaré problem, algebraic integrability and dicritical divisors | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | 10.1016/j.jde.2014.02.015 | |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca_CA |
dc.relation.publisherVersion | http://www.sciencedirect.com/science/article/pii/S0022039614000886?np=y | ca_CA |
dc.edition | Pre-print | ca_CA |
dc.type.version | info:eu-repo/semantics/sumittedVersion |
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