On the Formal Integrability Problem for Planar Differential Systems

On the Formal Integrability Problem for Planar Differential Systems

We study the analytic integrability problem through the formal integrability problem and we show its connection, in some cases, with the existence of invariant analytic (sometimes algebraic) curves. From the results obtained, we consider some families of analytic differential systems in ℂ2, and impo...

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Veröffentlicht in:Abstract and Applied Analysis 2013-01, Vol.2013 (2013), p.535-544-565
Hauptverfasser: Algaba, Antonio, García, Cristóbal, Giné, Jaume
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Computation
Integral calculus
Invariants
Joints
Mathematical analysis
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Zusammenfassung:We study the analytic integrability problem through the formal integrability problem and we show its connection, in some cases, with the existence of invariant analytic (sometimes algebraic) curves. From the results obtained, we consider some families of analytic differential systems in ℂ2, and imposing the formal integrability we find resonant centers obviating the computation of some necessary conditions.
ISSN:1085-3375
1687-0409
DOI:10.1155/2013/482305