2024
DOI: 10.3390/math12091338
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On the Integrability of Persistent Quadratic Three-Dimensional Systems

Brigita Ferčec,
Maja Žulj,
Matej Mencinger

Abstract: We consider a nine-parameter familiy of 3D quadratic systems, x˙=x+P2(x,y,z), y˙=−y+Q2(x,y,z), z˙=−z+R2(x,y,z), where P2,Q2,R2 are quadratic polynomials, in terms of integrability. We find necessary and sufficient conditions for the existence of two independent first integrals of corresponding semi-persistent, weakly persistent, and persistent systems. Unlike some of the earlier works, which primarily focus on planar systems, our research covers three-dimensional spaces, offering new insights into the complex … Show more

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