Zeitschrift für angewandte Mathematik und Physik

, Volume 64, Issue 5, pp 1443–1449 | Cite as

Invariant algebraic surfaces of the generalized Lorenz system

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Abstract

In this paper, according to the idea of the weight of a polynomial introduced by Swinnerton-Dyer(Math Proc Camb Philos Soc 132:385–393, 2002), we successfully find all the invariant algebraic surfaces of the generalized Lorenz system x′ = a(y − x), y′ = bx + cy − xz, z′ = xy + dz.

Mathematics Subject Classification (2010)

34A34 34C05 

Keywords

Darboux polynomials Invariant algebraic surface Cofactor Generalized Lorenz system 
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Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.College of Mathematics and EconometricsHunan UniversityChangshaPeople’s Republic of China
  2. 2.School of Information and MathematicsYangtze UniversityJingzhouPeople’s Republic of China

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