Structural stability of polynomial second order differential equations with periodic coefficients
Date
2004-08-09
Authors
Guzman, Adolfo W.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
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.
Description
Keywords
Singularity at infinity, Compactification, Structural stability, Second order differential equations
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.
Rights
Attribution 4.0 International