Structural stability of polynomial second order differential equations with periodic coefficients
| dc.contributor.author | Guzman, Adolfo W. | |
| dc.date.accessioned | 2021-04-26T19:29:12Z | |
| dc.date.available | 2021-04-26T19:29:12Z | |
| dc.date.issued | 2004-08-09 | |
| dc.description.abstract | This work characterizes the structurally stable second order differential equations of the form x'' = ni=0 αi(x)(x')i where ai : ℜ → ℜ are C<sup>r</sup> periodic functions. These equations have naturally the cylander M = S1 x ℜ as the phase space and are associated to the vector fields X(ƒ) = y ∂/∂x + ƒ(x, y) ∂/∂y, where ƒ(x, y) = ni=0αi(x)yi ∂/∂y. We apply a compactification to M as well as to X(ƒ) to study the behavior at infinity. For n ≥ 1, we define a set ∑n of X(ƒ) that is open and dense and characterizes the class of structural differential equations as above. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 28 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Guzman, A. W. (2004). Structural stability of polynomial second order differential equations with periodic coefficients. <i>Electronic Journal of Differential Equations, 2004</i>(98), pp. 1-28. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13452 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2004, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Singularity at infinity | |
| dc.subject | Compactification | |
| dc.subject | Structural stability | |
| dc.subject | Second order differential equations | |
| dc.title | Structural stability of polynomial second order differential equations with periodic coefficients | |
| dc.type | Article |