Computation of focus quantities of three-dimensional polynomial systemsRomanovski, Valery (Avtor) Shafer, Douglas (Avtor) integrabilityfocus quantitiescenter conditionsFix a collection of polynomial vector fields on $R^3$ with a singularity at the origin, for every one of which the linear part at the origin has two pure imaginary and one non-zero eigenvalue. Some such systems admit a local analytic first integral, which then defines a local center manifold of the system.Conditions for existence of a first integral are given by the vanishing certain polynomial or rational functions in the coefficients of the system called focus quantities. In this paper we prove that the focus quantities have a structure analogous to that in the two-dimensional case and use it to formulate an efficient algorithm for computing them.20142017-08-07 08:25:03Neznano67194ISSN: Y507-6781UDK: 517.9OceCobissID: 20968456COBISS_ID: 20981768ISSN pri članku: Y507-6781NUK URN: URN:SI:UM:DK:VFEI6KHAsl