On Sufficient Conditions for Integrability of a Planar System of ODEs Near a Degenerate Stationary Point

  • Victor Edneral
  • Valery G. Romanovski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6244)


We consider an autonomous system of ordinary differential equations, which is solved with respect to derivatives. To study the local integrability of the system near a degenerate stationary point we use an approach based on the Power Geometry Method and on the computation of resonant normal forms. For a planar system depending on five parameters we give four series of conditions on parameters of the system for which it is integrable near the degenerate stationary point.


planar ordinary differential equations integrability resonant normal form power geometry computer algebra 


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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Victor Edneral
    • 1
  • Valery G. Romanovski
    • 2
    • 3
  1. 1.Skobeltsyn Institute of Nuclear Physics of Lomonosov Moscow State UniversityRussia
  2. 2.CAMTP - Center for Applied Mathematics and Theoretical PhysicsUniversity of MariborMariborSlovenia
  3. 3.Faculty of Natural Science and MathematicsUniversity of MariborMariborSlovenia

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