A Preparation Theorem for a Class of Non-differentiable Functions with an Application to Hilbert's 16th Problem
| Affiliation auteurs | Affiliation ok |
| Titre | A Preparation Theorem for a Class of Non-differentiable Functions with an Application to Hilbert's 16th Problem |
| Type de publication | Book Chapter |
| Year of Publication | 2016 |
| Auteurs | Morsalani MEl, Mourtada A |
| Editor | Toni B |
| Book Title | MATHEMATICAL SCIENCES WITH MULTIDISCIPLINARY APPLICATIONS: IN HONOR OF PROFESSOR CHRISTIANE ROUSSEAU. AND IN RECOGNITION OF THE MATHEMATICS FOR PLANET EARTH INITIATIVE |
| Series Title | Springer Proceedings in Mathematics & Statistics |
| Volume | 157 |
| Pagination | 133-177 |
| Publisher | SPRINGER |
| City | 233 SPRING STREET, NEW YORK, NY 10013, UNITED STATES |
| ISBN Number | 978-3-319-31323-8; 978-3-319-31321-4 |
| ISBN | 2194-1009 |
| Mots-clés | Chebychev expansion, Hilbert 16th problem, Hyperbolic saddle point, Malgrange preparation theorem, Pseudo-isomorphism, Quasi-regular function |
| Résumé | We consider a class of unfoldings of quasi-regular functions. We assume that such perturbations have asymptotic developments which depend on many unfoldings of the logarithm function. We prove a preparation theorem for such functions; namely, they are ``conjugated'' to a finite principal part via a ``pseudoisomorphism''. This finite principal part is polynomial in the phase variable and these unfoldings of the logarithm function. As an application there exists a uniform bound in the parameter of the numbers of zeros of such class of non-differentiable functions. A finiteness result of the number of the limit cycles bifurcating from a perturbed hyperbolic polycycle is obtained too. |
| DOI | 10.1007/978-3-319-31323-8_8 |