Mathematics – Functional Analysis
Scientific paper
2001-02-09
Mathematics
Functional Analysis
110 pages, Ph-D thesis, in french
Scientific paper
Consider a singularly perturbed ordinary differential equation, admitting 0 as turning point of order p. We study the behaviour, in the complex plane, of the solutions of this equation in the neighborhood of 0. We prove that the domain of these solutions contains sectors like $\{\theta_1< \arg(x)<\theta_2, and |x|<|X_l| |\epsilon|^{1/(p+1)} \}$. If we introduce thereafter a p-parameter $\alpha$ in the equation, we have (for some particular values of the parameter, depending from $\epsilon$) canards solutions, id est solutions which are bounded in a whole neighborhood of the turning point. These two results are used for two examples, one of them is the Van der Pol equation; we can then find for these two equations an equivalent of the coefficients of the asymptotic serie in $\epsilon$ for the values of $\alpha$ corresponding to canards solutions.
No associations
LandOfFree
Etude d'equations differentielles singulierement perturbees au voisinage d'un point tournant 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 Etude d'equations differentielles singulierement perturbees au voisinage d'un point tournant, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Etude d'equations differentielles singulierement perturbees au voisinage d'un point tournant will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-613485