Formal Weierstrass nonintegrability criterion for some classes of polynomial differential systems in C²
Giné, Jaume (Universitat de Lleida. Departament de Matemàtica)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2020
Abstract:	In this paper, we present a criterion for determining the formal Weierstrass nonintegrability of some polynomial differential systems in the plane C². The criterion uses solutions of the form y = f(x) of the differential system in the plane and their associated cofactors, where f(x) is a formal power series. In particular, the criterion provides the necessary conditions in order that some polynomial differential systems in C² would be formal Weierstrass integrable. Inside this class there exist non-Liouvillian integrable systems. Finally we extend the theory of formal Weierstrass integrability to Puiseux Weierstrass integrability.
Grants:	Ministerio de Economía y Competitividad MTM2017-84383-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1276 Ministerio de Economía y Competitividad MTM2016-77278-P Ministerio de Economía y Competitividad MDM-2014-0445 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Weierstrass integrability ; Liouville integrability ; Polynomial differential systems
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 30, Issue 4 (March 2020) , art. 2050064, ISSN 1793-6551

DOI: 10.1142/S0218127420500649

Postprint 12 p, 664.4 KB

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