Canard Cycles and Center Manifolds

Freddy Dumortier · Robert H. Roussarie

1996年1月 · American Mathematical Society: Memoirs of the American Mathematical Society 第 577 冊 · American Mathematical Soc.

電子書

100

頁數

評分和評論未經驗證瞭解詳情

關於這本電子書

This important paper is destined to be cited more often for the innovative techniques that are introduced rather than for the specific results that are proved. The proofs of the asymptotic formulas and the geometric explanation of the canard phenomenon are all highly nontrivial, while making use of center manifold theory, normal forms, foliations, Abelian integrals, asymptotic series and desingularization by weighted blow-up. The desingularization technique is particularly interesting and involves a construction for blow-up of parametrized families of vector fields, a rather far-reaching generalization of the blow-up construction for a fixed singularity. In fact, the blow-up of a parametrized family of vector fields yields a new geometric object that the authors call a foliated local vector field. This concept generalizes the idea of rescaling a differential equation and thus should be very useful in the analysis of many other singular perturbation problems.