The Poincaré problem, algebraic integrability and dicritical divisors
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONMetadata
Title
The Poincaré problem, algebraic integrability and dicritical divisorsDate
2015-07-01xmlui.dri2xhtml.METS-1.0.item-edition
Pre-printISSN
0022-0396Type
info:eu-repo/semantics/articlePublisher version
http://www.sciencedirect.com/science/article/pii/S0022039614000886?np=yVersion
info:eu-repo/semantics/sumittedVersionSubject
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 ... [+]
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. [-]
Is part of
Journal of Differential Equations, 2014, 256.11: 3614-3633Rights
Copyright © 2014 Elsevier Ltd. All rights reserved
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info:eu-repo/semantics/openAccess
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- MAT_Articles [751]