Pseudo-Abelian integrals: unfolding generic exponential case
| dc.creator | Bobienski, Marcin | |
| dc.creator | Mardesic, Pavao | |
| dc.creator | Novikov, Dmitry | |
| dc.date | 2009-03-15 | |
| dc.date.accessioned | 2026-07-07T12:52:48Z | |
| dc.date.available | 2026-07-07T12:52:48Z | |
| dc.description | We consider an integrable polynomial system with generalized Darboux first integral H_0. We assume that it defines a family of real cycles in a region bounded by a polycycle. To any polynomial form ηone can associate the pseudo-abelian integrals I(h), which is the first order term of the displacement function of the system perturbed by η. We consider Darboux first integrals unfolding H_0 (and its saddle-nodes) and pseudo-abelian integrals associated to these unfoldings. Under genericity assumptions we show the existence of a uniform local bound for the number of zeros of these pseudo-abelian integrals. The result is part of a program to extend Varchenko-Khovanskii's theorem from abelian integrals to pseudo-abelian integrals and prove the existence of a bound for the number of their zeros in function of the degree of the polynomial system only. | |
| dc.identifier | https://arxiv.org/abs/0903.2673 | |
| dc.identifier | http://arxiv.org/abs/0903.2673 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223414 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 34C07, 34C08 | |
| dc.title | Pseudo-Abelian integrals: unfolding generic exponential case | |
| dc.type | text |