Local Integrating Factors
Copyright policy )Local Integrating Factors
The authors consider the differential equation \(\dot{x}=f(x)\) in \(\mathbb{C}^2\), where \(f\) is an analytic or formal vector field and continues his investigations on the existence of local integrating factors near a stationary point. Two classes of degenerate stationary points are considered. The first one has a nilpotent linear part. It is proved that in this case there exists an integrating factor only if a certain polynomial in the Taylor coefficients of the vector field vanishes. The second one has a vanishing linearization and none of the stationary points obtained as a result of blowing up is dicritical. In this case, in general, there are no formal integrating factors.
degenerate stationary point, integrating factors, blow up, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Symmetries, invariants of ordinary differential equations
degenerate stationary point, integrating factors, blow up, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Symmetries, invariants of ordinary differential equations
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!