Remark on a conjecture of Kaplan and Yorke

Angelika W{örz-Busekros
1982 Proceedings of the American Mathematical Society  
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
more » ... ntial equations in R™ which possesses at least one stationary solution x*. After a preliminary translation x* !-► 0 the system can be written as fc=i Received by the editors September 14, 1981September 14, . 1980 Mathematics Subject Classification. Primary 34C05. Key words and phrases. Inhomogeneous and homogeneous quadratic differential equations.
doi:10.1090/s0002-9939-1982-0656107-6 fatcat:et2tudch25gdpjajhoezr6cdvu