Rational first integrals in the Darboux theory of integrability in C^n
By Jaume Llibre, Xiang Zhang. 2010
69 citations recorded by the source corpus.
Abstract In 1979 Jouanolou showed that if the number of invariant algebraic hypersurfaces of a polynomial vector field in R n or C n of degree d is at least ( d + n − 1 n ) + n , then the vector field has a rational first integral. His proof used sophisticated tools of algebraic geometry. We provide an easy and elementary proof of Jouanolou's result using linear algebra.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/be84c6631a0949ca6373ad187a7a30379fecdad1
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In Algebra and Number Theory
In Geometry and Topology
- Xiang Zhang
- Jaume Llibre
- Maite Grau
- Isaac A. García
- Douglas Duarte Novaes
- Maoan Han
- Cláudia Valls
- Jaume Giné Mesa
In Statistical and Nonlinear Physics
- Xiang Zhang
- Jaume Llibre
- Maite Grau
- Maoan Han
- Douglas Duarte Novaes
- Isaac A. García
- Cláudia Valls
- Jaume Giné Mesa
Citations in the corpus
- On the Darboux Integrability of Polynomial Differential Systems (2012, background): “This characterization due to Llibre and Zhang [28] extends the algebraic multiplicity introduced by Christopher, Llibre and Pereira in [11] for invariant algebraic curves of C2 to invariant algebraic hypersurfaces of Cn.”