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.
Orbital reducibility and a generalization of lambda symmetries / G. Cicogna, G. Gaeta, S. Walcher. - In: JOURNAL OF LIE THEORY. - ISSN 0949-5932. - 23:2(2013 Jun), pp. 357-381.
Orbital reducibility and a generalization of lambda symmetries
G. GaetaSecondo
;
2013
Abstract
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.
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