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Titolo:
ON THE NONEXISTENCE OF CONSTANTS OF DERIVATIONS - THE PROOF OF A THEOREM OF JOUANOLOU AND ITS DEVELOPMENT
Autore:
OLLAGNIER JM; NOWICKI A; STRELCYN JM;
Indirizzi:
ECOLE POLYTECH,CTR MATH,GAGE,CNRS,UA 169 F-91128 PALAISEAU FRANCE NICHOLAS COPERNICUS UNIV,INST MATH PL-87100 TORUN POLAND UNIV ROUEN,DEPT MATH,CNRS,UA 1378 F-76821 MONT ST AIGNAN FRANCE UNIV PARIS 13,INST GALLILEE,ANAL GEOMETRIE & APPLICAT LAB,CNRS,UA 742F-93430 VILLETANEUSE FRANCE
Titolo Testata:
Bulletin des sciences mathematiques
fascicolo: 3, volume: 119, anno: 1995,
pagine: 195 - 233
SICI:
0007-4497(1995)119:3<195:OTNOCO>2.0.ZU;2-1
Fonte:
ISI
Lingua:
ENG
Soggetto:
DIFFERENTIAL-EQUATIONS; INTEGRALS;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
CompuMath Citation Index
Science Citation Index Expanded
Citazioni:
21
Recensione:
Indirizzi per estratti:
Citazione:
J.M. Ollagnier et al., "ON THE NONEXISTENCE OF CONSTANTS OF DERIVATIONS - THE PROOF OF A THEOREM OF JOUANOLOU AND ITS DEVELOPMENT", Bulletin des sciences mathematiques, 119(3), 1995, pp. 195-233

Abstract

Inspired by the proof of JOUANOLOU'S non-integrability theorem, we describe a method for proving the non-existence of non-trivial constantsof some derivations in polynomial rings K [x(1), ..., x(n)], where K is a field of characteristic 0. In some cases, even the non-existence of non-trivial constants of derivations in quotient field K (x(1), ..., x(n)) can be proved. When K = R or C, this is equivalent to proving the non-existence of polynomial, respectively rational, first integrals for some systems of polynomial ordinary differential equations. Several examples, among which JOUANOLOU'S one, are described in details.

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Documento generato il 29/09/20 alle ore 07:08:55