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Polynomial differential systems having a given Darbouxian first integral

โœ Scribed by Jaume Llibre; Chara Pantazi


Book ID
108075649
Publisher
Elsevier Science
Year
2004
Tongue
French
Weight
131 KB
Volume
128
Category
Article
ISSN
0007-4497

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We consider in this work planar polynomial differential systems having a polynomial first integral. We prove that these systems can be obtained from a linear system through a polynomial transformation of variables.

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We classify all the global phase portraits of the quadratic polynomial vector fields having a rational first integral of degree 2. In other words we characterize all the global phase portraits of the quadratic polynomial vector fields having all their orbits contained in conics. For such a vector fi