Abstract
We consider an autonomous system of ordinary differential equations, which is resolved with respect to derivatives. To study local integrability of the system near a degenerate stationary point, we use an approach based on Power Geometry and on the computation of the resonant normal form. For the particular non-Hamilton 5-parameter case of concrete planar system, we found previously the almost complete set of necessary conditions on parameters of the system for which the system is locally integrable near a degenerate stationary point. These sets of parameters, satisfying the conditions, consist of 4 two-parameter subsets in this 5-parameter space except 1 special hyper plane b 2 = 2/3. We wrote down 4 first integrals of motion as functions of the system parameters. Here we have proved that the limitation b 2 ≠ 2/3 can be excluded from the previously obtained solutions. Now we have not found the additional first integrals.
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Bruno, A.D., Edneral, V.F. (2013). On Possibility of Additional Solutions of the Degenerate System Near Double Degeneration at the Special Value of the Parameter. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2013. Lecture Notes in Computer Science, vol 8136. Springer, Cham. https://doi.org/10.1007/978-3-319-02297-0_6
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DOI: https://doi.org/10.1007/978-3-319-02297-0_6
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