Strongly formal Weierstrass non-integrability for polynomial differential systems in C2
Recently a criterion has been given for determining the weakly formal Weierstrass non-integrability of polynomial differential systems in C2 . Here we extend this criterion for determining the strongly formal Weierstrass non-integrability which includes the weakly formal Weierstrass non-integrabilit...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2020
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Liouville integráció, Weierstrass integráció, Differenciaegyenlet |
| doi: | 10.14232/ejqtde.2020.1.1 |
| Online Access: | http://acta.bibl.u-szeged.hu/66419 |
| Tartalmi kivonat: | Recently a criterion has been given for determining the weakly formal Weierstrass non-integrability of polynomial differential systems in C2 . Here we extend this criterion for determining the strongly formal Weierstrass non-integrability which includes the weakly formal Weierstrass non-integrability of polynomial differential systems in C2 . The criterion is based on the solutions of the form y = f(x) with f(x) ∈ C[[x]] of the differential system whose integrability we are studying. The results are applied to a differential system that contains the famous force-free Duffing and the Duffing–Van der Pol oscillators. |
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| ISSN: | 1417-3875 |