Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899578 | Journal of Mathematical Analysis and Applications | 2018 | 8 Pages |
Abstract
Given mâ¥1 and a smooth family of planar vector fields (Xε)ε that is a perturbation of a period annulus, we provide a characterization, in terms of Lie brackets, of the property that the first (mâ1) Melnikov functions of (Xε)ε vanish identically. The equivalent condition is the existence of a smooth family of planar vector fields (Uε)ε, called here perturbed normalizers of order m. We also provide an effective procedure for computing Uε when the first (mâ1) Melnikov functions of (Xε)ε vanish identically. A formula for the derivative of the m-th order Melnikov function is given.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Adriana BuicÄ,