Recent Applications of the Theory of Lie Systems in Ermakov Systems

Details Recent Applications of the Theory of Lie Systems in Ermakov Systems Recent Applications of the Theory of Lie Systems in Ermakov Systems

2008-03-12

arxiv.org/abs/0803.1824v1

SIGMA 4 (2008), 031, 18 pages

Physics

Mathematical Physics

This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (Ju

Scientific paper

10.3842/SIGMA.2008.031

We review some recent results of the theory of Lie systems in order to apply such results to study Ermakov systems. The fundamental properties of Ermakov systems, i.e. their superposition rules, the Lewis-Ermakov invariants, etc., are found from this new perspective. We also obtain new results, such as a new superposition rule for the Pinney equation in terms of three solutions of a related Riccati equation.

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