Multiplicity of Invariant Algebraic Curves and Darboux Integrability

Details Multiplicity of Invariant Algebraic Curves and Darboux Integrability Multiplicity of Invariant Algebraic Curves and Darboux Integrability

2000-09-02

arxiv.org/abs/math/0009020v1

Mathematics

Dynamical Systems

16 pages, LaTeX

Scientific paper

We define four different kinds of multiplicity of an invariant algebraic
curve for a given polynomial vector field and investigate their relationships.
After taking a closer look at the singularities and at the line of infinity, we
improve the Darboux theory of integrability using these new notions of
multiplicity.

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