Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 136, pp. 1-6.

Title: Centers on center manifolds in a quadratic system obtained from
       a scalar third-order differential equation

Authors: Warley Ferreira da Cunha (Univ. Federal de Itajuba, MG, Brazil)
         Fabio Scalco Dias    (Univ. Federal de Itajuba, MG, Brazil)
	 Luis Fernando Mello  (Univ. Federal de Itajuba, MG, Brazil)

Abstract: 
 We give affirmative answers to two questions
 concerning the existence of centers on
 local center manifolds at equilibria of a
 quadratic system in the three dimensional space.
 These questions were posed by Dias and Mello [1]
 when studying a scalar third-order differential equation.

Submitted September 29, 2011. Published October 19, 2011.
Math Subject Classifications: 34C40, 34C15, 34C60, 34C25.
Key Words: Center; center manifold; invariant algebraic surface;
           quadratic system.