A BLOW-UP METHOD TO PROVE FORMAL INTEGRABILITY FOR SOME PLANAR DIFFERENTIAL SYSTEMS

Brigita Ferčec; Jaume Giné

doi:10.11948/2018.1833

2018 Volume 8 Issue 6

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Brigita Ferčec, Jaume Giné. A BLOW-UP METHOD TO PROVE FORMAL INTEGRABILITY FOR SOME PLANAR DIFFERENTIAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2018, 8(6): 1833-1850. doi: 10.11948/2018.1833

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Brigita Ferčec, Jaume Giné. A BLOW-UP METHOD TO PROVE FORMAL INTEGRABILITY FOR SOME PLANAR DIFFERENTIAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2018, 8(6): 1833-1850. doi: 10.11948/2018.1833

A BLOW-UP METHOD TO PROVE FORMAL INTEGRABILITY FOR SOME PLANAR DIFFERENTIAL SYSTEMS

1 Faculty of Energy Technology, University of Maribor, Hočevarjev trg 1, 8270 Krško, Slovenia;
2 Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia;
3 Departament de Matemàtica, Inspires Research Centre, Universitat de Lleida, Avda. Jaume Ⅱ, 69;25001 Lleida, Catalonia, Spain

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Abstract

Abstract

In this work we provide an effective method to prove the formal integrability of the resonant saddles. The method is based on the use of a blow-up and the resolution of a recurrence differential equation using induction. Using the method some open integrability problems for certain resonant saddles are solved.
- Saddle constants /
- formal first integral /
- invariant analytic curve
MSC: 34C05;37G05;34C20

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References

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