Pith. sign in

REVIEW

Liouvillian integrability of polynomial differential systems

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1311.7255 v1 pith:LPKL6UOG submitted 2013-11-28 math.DS

Liouvillian integrability of polynomial differential systems

classification math.DS
keywords differentialliouvillianpolynomialdarbouxintegrabilitysystemsdimensionalfirst
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
read the original abstract

M.F. Singer [Liouvillian first integrals of differential equations, Trans. Amer. Math. Soc. 333 (1992), 673--688] proved the equivalence between Liouvillian integrability and Darboux integrability for two dimensional polynomial differential systems. In this paper we will extend Singer's result to any finite dimensional polynomial differential systems. We prove that if an n--dimensional polynomial differential system has n-1 functionally independent Darboux Jacobian multiplier then it has n-1 functionally independent Liouvillian first integrals. Conversely if the system is Liouvillian integrable then it has a Darboux Jacobian multiplier.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.