Approximation of the domain of attraction of an asymptotically stable fixed point of a first order analytical system of difference equations
| dc.creator | Kaslik, E. | |
| dc.creator | Balint, A. M. | |
| dc.creator | Birauas, S. | |
| dc.creator | Balint, St. | |
| dc.date | 2003-02-27 | |
| dc.date | 2003-03-05 | |
| dc.date.accessioned | 2026-07-07T04:55:37Z | |
| dc.date.available | 2026-07-07T04:55:37Z | |
| dc.description | In this paper a first order analytical system of difference equations is considered. For an asymptotically stable fixed point x0 of the system a gradual approximation of the domain of attraction DA is presented in the case when the matrix of the linearized system in x0 is a contraction. This technique is based on the gradual extension of the "embryo" of an analytic function of several variables. The analytic function is a Lyapunov function whose natural domain of analyticity is the DA and which satisfies an iterative functional equation. The equation permits to establish an "embryo" of the Lyapunov function and a first approximation of the DA. The "embryo" is used for the determination of a new "embryo" and a new part of the DA. In this way, computing new "embryos" and new domains, the DA is gradually approximated. Numerical examples are given for polynomial systems. | |
| dc.description | 11 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/math/0302338 | |
| dc.identifier | http://arxiv.org/abs/math/0302338 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66643 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 34K20 | |
| dc.title | Approximation of the domain of attraction of an asymptotically stable fixed point of a first order analytical system of difference equations | |
| dc.type | text |