A Necessary Condition for existence of Lie Symmetries in Quasihomogeneous Systems of Ordinary Differential Equations

Details A Necessary Condition for existence of Lie Symmetries in Quasihomogeneous Systems of Ordinary Differential Equations A Necessary Condition for existence of Lie Symmetries in Quasihomogeneous Systems of Ordinary Differential Equations

2001-04-24

arxiv.org/abs/math/0104215v1

Mathematics

Dynamical Systems

15 pages, no figures, AMSLaTeX

Scientific paper

10.1143/JPSJ.71.2396

Lie symmetries for ordinary differential equations are studied. In systems of ordinary differential equations, there do not always exist non-trivial Lie symmetries around equilibrium points. We present a necessary condition for existence of Lie symmetries analytic in the neighbourhood of an equilibrium point. In addition, this result can be applied to a necessary condition for existence of a Lie symmetry in quasihomogeneous systems of ordinary differential equations. With the help of our main theorem, it is proved that several systems do not possess any analytic Lie symmetries.

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