Let X be a germ of holomorphic vector field at the origin of C and vanishing there. We assume that X is a “nondegenerate” good perturbation of a singular completely integrable system. The latter is associated to a family of linear diagonal vector fields which is assumed to have nontrivial polynomial first integrals. We show that X admits many invariant analytic subsets in a neighborhood of the ...

Folded saddle-nodes occur generically in one parameter families of singularly perturbed systems with two slow variables. We show that these folded singularities are the organizing centers for two main delay phenomena in singular perturbation problems: canards and delayed Hopf bifurcations. We combine techniques from geometric singular perturbation theory – the blow-up technique – and from delay...

This contribution presents a new method of analyzing the dynamics of a biological relevant neural network with different time scales based on the theory of flow invariance. We are able to show that the resulting stability conditions are less restrictive and more general than with K-monotone theory or singular perturbation theory. The theoretical results are further substantiated by simulation r...

Some quantum mechanical potentials, singular at short distances, lead to ultraviolet divergences when used in perturbation theory. Exactly as in quantum field theory, but much simpler, regularization and renormalization lead to finite physical results, which compare correctly to the exact ones. The Dirac delta potential, because of its relevance to triviality, and the AharonovBohm potential, be...

v Acknowledgments vi Chapter

this paper a novel homotopy perturbation method has been presented for forced convection boundary layer problems in a porous medium. Noting the infinite condition, a homotopy form which is similar to the singular perturbation form has been considered. The inner and outer solutions have been achieved and the coincidence of the results has been investigated with a proper matching method. The resu...