Analytical integrability problem for perturbations of cubic Kolmogorov systems

作者：Algaba Antonio; Garcia Cristobal; Reyes Manuel^*

来源：Chaos Solitons & Fractals, 2018, 113: 1-10.

DOI：10.1016/j.chaos.2018.05.011

• Kolmogorov systems
• Integrability
• Linearization
• Inverse Integrating Factors

We solve, by using normal forms, the analytical integrability problem for differential systems in the plane whose first homogeneous component is a cubic Kolmogorov system whose origin is an isolated singularity. As an application, we give the analytically integrable systems of a class of systems (x) over dot = x(P-2 + P-3), (y) over dot = y(Q(2) + Q(3)), with P-i, Q(i) homogeneous polynomials of degree i. We also prove that for any n >= 3, there are analytically integrable perturbations of (x) over dot = xP(n), (y) over dot = yQ(n) which are not orbital equivalent to its first homogeneous component.

• 出版日期2018-8