On New Integrals of the Algaba-Gamero-Garcia System

We study local integrability of a plane autonomous polynomial system of ODEs depending on five parameters with a degenerate singular point at the origin. The approach is based on making use of the Power Geometry Method and the computation of normal forms. We look for the complete set of necessary conditions on parameters of the system under which the system is locally integrable near the degenerate stationary point. We found earlier that the sets of parameters satisfying these conditions consist of four two-parameter subsets in the full five-parameter co-space. Now we consider the special subcase of the case b^2 = 2/3 and separate subsubcases when additional first integrals can exist. Here we have found two such integrals. © 2017, Springer International Publishing AG.

Authors
Bruno A.D.1 , Edneral V.F. 2, 3 , Romanovski V.G.4, 5, 6
Language
English
Pages
40-50
Status
Published
Volume
10490 LNCS
Year
2017
Organizations
  • 1 Keldysh Institute of Applied Mathematics of RAS, Miusskaya Sq. 4, Moscow, 125047, Russian Federation
  • 2 Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Leninskie Gory 1(2), Moscow, 119991, Russian Federation
  • 3 Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow, 117198, Russian Federation
  • 4 Faculty of Electrical Engineering and Computer Science, University of Maribor, Smetanova 17, Maribor, SI-2000, Slovenia
  • 5 CAMTP – Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, Maribor, SI-2000, Slovenia
  • 6 Faculty of Natural Science and Mathematics, University of Maribor, Koroška cesta 160, Maribor, SI-2000, Slovenia
Keywords
Computer algebra; Integrability; Ordinary differential equations; Power Geometry; Resonant normal form
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/6347/
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