Phase portraits for quadratic homogeneous polynomial vector fields on S^2

Details Phase portraits for quadratic homogeneous polynomial vector fields on S^2 Phase portraits for quadratic homogeneous polynomial vector fields on S^2

2008-10-15

arxiv.org/abs/0810.2754v1

Mathematics

Dynamical Systems

35 pages

Scientific paper

Let X be a homogeneous polynomial vector field of degree 2 on S^2. We show that if X has at least a non--hyperbolic singularity, then it has no limit cycles. We give necessary and sufficient conditions for determining if a singularity of X on S^2 is a center and we characterize the global phase portrait of X modulo limit cycles. We also study the Hopf bifurcation of X and we reduce the 16^{th} Hilbert's problem restricted to this class of polynomial vector fields to the study of two particular families. Moreover, we present two criteria for studying the nonexistence of periodic orbits for homogeneous polynomial vector fields on S^2 of degree n.

Affiliated with

Also associated with

No associations

Rating

Phase portraits for quadratic homogeneous polynomial vector fields on S^2 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Phase portraits for quadratic homogeneous polynomial vector fields on S^2, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Phase portraits for quadratic homogeneous polynomial vector fields on S^2 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-303684