Structural stability of polynomial second order differential equations with periodic coefficients
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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 Cr 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=0 αi(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.
CitationGuzman, A. W. (2004). Structural stability of polynomial second order differential equations with periodic coefficients. Electronic Journal of Differential Equations, 2004(98), pp. 1-28.
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