Mathematics – Dynamical Systems
Scientific paper
2012-03-08
Mathematics
Dynamical Systems
Scientific paper
A practical method is described for computing the generators of the algebra of first integrals that works well for a large family of Hopf-Zero singularity systems. A Lie algebra description is presented for all volume-preserving classical normal form of Hopf-Zero singularity systems. This is a maximal vector space of classical normal forms with first integral; this is whence our approach works. Systems with a non-zero condition on their quadratic part are considered. The algebra of all first integrals for any such system has a unique (modulo scalar multiplication) generator. The infinite level volume-preserving parametric normal forms of any non-degenerate perturbation within the Lie algebra of any such system is computed, where it can have rich dynamics. The associated unique generator of the algebra of first integrals are computed. The symmetry group of the infinite level normal forms are also discussed. Some necessary formulas are derived and implemented on appropriately modified R\"{o}ssler and generalized Kuramoto-Sivashinsky equations to demonstrate the applicability of our theoretical results.
Gazor Majid
Mokhtari Fahimeh
No associations
LandOfFree
Volume-preserving normal forms of Hopf-Zero singularity 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 Volume-preserving normal forms of Hopf-Zero singularity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Volume-preserving normal forms of Hopf-Zero singularity will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-17442