Mathematics – Dynamical Systems
Scientific paper
2004-04-26
Mathematics
Dynamical Systems
23 pages, 2 figures
Scientific paper
This paper includes results centered around three topics, all of them related with the nonlinear stability of equilibria in Poisson dynamical systems. Firstly, we prove an energy-Casimir type sufficient condition for stability that uses functions that are not necessarily conserved by the flow and that takes into account certain asymptotically stable behavior that may occur in the Poisson category. This method is adapted to Poisson systems obtained via a reduction procedure and we show in examples that the kind of stability that we propose is appropriate when dealing with the stability of the equilibria of some constrained systems. Finally, we discuss two situations in which the use of continuous Casimir functions in stability studies is equivalent to the topological stability methods introduced by Patrick {\it et al.}
Ortega Juan-Pablo
Planas-Bielsa Víctor
Ratiu Tudor S.
No associations
LandOfFree
Asymptotic and Lyapunov stability of Poisson equilibria 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 Asymptotic and Lyapunov stability of Poisson equilibria, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotic and Lyapunov stability of Poisson equilibria will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-630764