Integrability Conditions for Complex Homogeneous Kukles Systems
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Date
2018
Authors
Giné, Jaume
Valls, Claudia
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In this paper we study the existence of local analytic first integrals for complex polynomial differential systems of the form ẋ = x + Pn(x, y), ẏ = −y, where Pn(x,y) is a homogeneous polynomial of degree n, called the complex homogeneous Kukles systems of degree n. We characterize all the homogeneous Kukles systems of degree n that belong to the Sibirsky ideal. Finally, we provide necessary and sufficient conditions when n = 2,...,7 in order that the complex homogeneous Kukles system has a local analytic first integral computing the saddle constants and using Gröbner bases to find the decomposition of the algebraic variety into its irreducible components.
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Journal of Nonlinear Mathematical Physics, 2018, vol. 25, núm. 3, p. 387-398