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Journal of Lie Theory 23 (2013), No. 2, 357--381
Copyright Heldermann Verlag 2013

Orbital Reducibility and a Generalization of Lambda Symmetries

Giampaolo Cicogna
Dip. di Fisica, via Buonarroti 2, 56127 Pisa, Italy

Giuseppe Gaeta
Dip. di Matematica, Università degli Studi di Milano, via Saldini 50, 20133 Milano, Italy

Sebastian Walcher
Lehrstuhl A für Mathematik, RWTH Aachen, 52056 Aachen, Germany

We review the notion of reducibility and we introduce and discuss the notion of orbital reducibility for autonomous ordinary differential equations of first order. The relation between (orbital) reducibility and (orbital) symmetry is investigated and employed to construct (orbitally) reducible systems. By standard identifications, the notions extend to non-autonomous ODEs of first and higher order. Moreover we thus obtain a generalization of the lambda symmetries of Muriel and Romero. Several examples are given.

Keywords: Symmetry, reduction, vector field.

MSC: 34A05, 34C14, 34A25, 34A26

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