On the rate of convergence of periodic solutions in perturbed autonomous systems as the perturbation vanishes
| dc.creator | Makarenkov, Oleg | |
| dc.creator | Nistri, Paolo | |
| dc.date | 2007-09-27 | |
| dc.date.accessioned | 2026-07-07T08:32:38Z | |
| dc.date.available | 2026-07-07T08:32:38Z | |
| dc.description | We consider an autonomous system in R^n having a limit cycle x_0 of period T>0 which is nondegenerate in a suitable sense. We then consider the perturbed system obtained by adding to the autonomous system a T-periodic, not necessarily differentiable, term whose amplitude tends to 0 as a small parameter e>0 tends to 0. Assuming the existence of a T-periodic solution x_e of the perturbed system and its convergence to x_0 as e->0, the paper establishes the existence of d_e->0 as e->0 such that \|x_e(t+d_e)-x_0(t)\|<=eM for some M>0 and any e>0 sufficiently small. | |
| dc.description | To Appear in Commun. Pure Appl. Anal | |
| dc.identifier | https://arxiv.org/abs/0709.4431 | |
| dc.identifier | http://arxiv.org/abs/0709.4431 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138854 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 34A10, 34C24 | |
| dc.title | On the rate of convergence of periodic solutions in perturbed autonomous systems as the perturbation vanishes | |
| dc.type | text |