We characterize the set of $n$-jets admitting an extension which is a germ of a differential equation with an analytic first integral, and compute its codimension in the $n$-jet space. Some applications in the case of the centre-focus problem are given.
Jets of differential equations having integrable extensions / Villarini, Massimo. - In: ERGODIC THEORY & DYNAMICAL SYSTEMS. - ISSN 0143-3857. - STAMPA. - 18:(1998), pp. 1527-1544.
Jets of differential equations having integrable extensions
VILLARINI, Massimo
1998
Abstract
We characterize the set of $n$-jets admitting an extension which is a germ of a differential equation with an analytic first integral, and compute its codimension in the $n$-jet space. Some applications in the case of the centre-focus problem are given.
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