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Remark on a conjecture of Kaplan and Yorke

1982
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Proceedings of the American Mathematical Society
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If all solutions of a system of quadratic differential equations with at least one stationary solution are bounded, then the corresponding homogeneous equation possesses a line of stationary points. The purpose of this note is to show that a conjecture of Kaplan and Yorke on the relationship between the behavior of solutions of a system of quadratic differential equations and of the associated homogeneous system is true. Let us consider a system of nonlinear quadratic differential equations in

doi:10.1090/s0002-9939-1982-0656107-6
fatcat:et2tudch25gdpjajhoezr6cdvu