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Journal of Lie Theory 25 (2015), No. 1, 125--146
Copyright Heldermann Verlag 2015



Side Conditions for Ordinary Differential Equations

Giampaolo Cicogna
Dipartimento di Fisica, UniversitÓ di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy
cicogna@df.unipi.it

Giuseppe Gaeta
Dipartimento di Matematica, UniversitÓ degli Studi di Milano, via Saldini 50, 20133 Milano, Italy
giuseppe.gaeta@unimi.it

Sebastian Walcher
Lehrstuhl A fŘr Mathematik, RWTH Aachen, 52056 Aachen, Germany
walcher@matha.rwth-aachen.de



We specialize Olver's and Rosenau's side condition heuristics for the determination of particular invariant sets of ordinary differential equations. It turns out that side conditions of so-called LaSalle type are of special interest. Moreover we put side condition properties of symmetric and partially symmetric equations in a wider context. In the final section we present an application to parameter-dependent systems, in particular to quasi-steady state for chemical reactions.

Keywords: Invariant set, Lie series, infinitesimal symmetry, quasi-steady state, QSS.

MSC: 34A05, 34C14, 34C45, 92C45

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