Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
1999-11-03
Nonlinear Sciences
Exactly Solvable and Integrable Systems
PlainTeX, no figures
Scientific paper
We consider dynamical systems depending on one or more real parameters, and assuming that, for some ``critical'' value of the parameters, the eigenvalues of the linear part are resonant, we discuss the existence -- under suitable hypotheses -- of a general class of bifurcating solutions in correspondence to this resonance. These bifurcating solutions include, as particular cases, the usual stationary and Hopf bifurcations. The main idea is to transform the given dynamical system into normal form (in the sense of Poincar\'e-Dulac), and to impose that the normalizing transformation is convergent, using the convergence conditions in the form given by A. Bruno. Some specially interesting situations, including the cases of multiple-periodic solutions, and of degenerate eigenvalues in the presence of symmetry, are also discussed with some detail.
No associations
LandOfFree
Resonant Bifurcations 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 Resonant Bifurcations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Resonant Bifurcations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-554341