General Relativity and Gravitation

, Volume 23, Issue 12, pp 1363–1383 | Cite as

Algebraic invariant curves in cosmological dynamical systems and exact solutions

  • C. G. Hewitt
Research Articles


The Einstein field equations for a number of classes of cosmological models have previously been written as polynomial systems of ordinary differential equations. We show that, for restricted parameter values, these equations admit algebraic invariant curves, which, in turn, lead to exact solutions of the field equations. This property explains the recent discovery of a number of exact solutions and is used to produce additional ones.


Differential Equation Dynamical System Exact Solution Ordinary Differential Equation Field Equation 
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Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • C. G. Hewitt
    • 1
  1. 1.Department of Applied MathematicsUniversity of WaterlooCanada

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