Electron. J. Diff. Equ., Vol. 2011 (2011), No. 136, pp. 1-6.

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

Warley Ferreira da Cunha, Fabio Scalco Dias, Luis Fernando Mello

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.

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Warley Ferreira da Cunha
Instituto de Ciências Exatas, Universidade Federal de Itajubá
Avenida BPS 1303, Pinheirinho, CEP 37.500-903
Itajubá, MG, Brazil
email: warleycunha@unifei.edu.br
Fabio Scalco Dias
Instituto de Ciências Exatas, Universidade Federal de Itajubá
Avenida BPS 1303, Pinheirinho, CEP 37.500-903
Itajubá, MG, Brazil
email: scalco@unifei.edu.br
Luis Fernando Mello
Instituto de Ciências Exatas, Universidade Federal de Itajubá
Avenida BPS 1303, Pinheirinho, CEP 37.500-903
Itajubá, MG, Brazil
Tel: 00-55-35-36291217, Fax: 00-55-35-36291140
email: lfmelo@unifei.edu.br

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