Open AccessON THE INTEGRABILITY OF THE DIFFERENTIAL SYSTEMS IN DIMENSION TWO AND OF THE POLYNOMIAL DIFFERENTIAL SYSTEMS IN ARBITRARY DIMENSION
Author(s) -
Jaume Llibre
Publication year - 2011
Publication title -
journal of applied analysis and computation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.55
H-Index - 21
eISSN - 2158-5644
pISSN - 2156-907X
DOI - 10.11948/2011004
Subject(s) - dimension (graph theory) , polynomial , mathematics , differential (mechanical device) , mathematical analysis , pure mathematics , physics , thermodynamics
This is a survey on recent results providing sufficient conditions for the existence of a first integral, first for vector fields defined on real surfaces, and second for polynomial vector fields in \(R^n\) or \(C^n\) with \(n\geq 2\). We also provide an open question and some applications based on the existence of such first integrals.
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