Formal first integrals along solutions of differential systems I

Authors:
Ainhoa Aparicio-Monforte;Moulay A. Barkatou;Sergi Simon;Jacques-Arthur Weil
Affiliations:
Johannes Kepler University, Linz, Austria;Université de Limoges, Limoges, France;University of Portsmouth, Portsmouth, United Kingdom;Université de Limoges, Limoges, France
Venue:
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Year:
2011

Citing 3
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Abstract

We consider an analytic vector field x = X(x\right) and study, via a variational approach, whether it may possess analytic first integrals. We assume one solution Γ is known and we study the successive variational equations along Γ. Constructions in [MRRS07] show that Taylor expansion coefficients of first integrals appear as rational solutions of the dual linearized variational equations. We show that they also satisfy linear "filter" conditions. Using this, we adapt the algorithms from [Bar99, vHW97] to design new ones optimized to this effect and demonstrate their use. Part of this work stems from the first author's Ph.D. thesis1 [AM10].