Аннотация: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. Early we found 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 found two such integrals.