Algaba Durán, AntonioGarcía García, Cristóbal, MatemáticoReyes Columé, Manuel2022-10-142022-10-142022Algaba, A., García, C., & Reyes, M. (2022). Analytic partial-integrability of a symmetric Hopf-zero degeneracy. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1-20. doi:10.1017/prm.2022.190308-21051473-7124 (electrónico)http://hdl.handle.net/10272/21253We deal with analytic three-dimensional symmetric systems whose origin is a Hopf-zero singularity. Once it is not completely analytically integrable, we provide criteria on the existence of at least one functionally independent analytic first integral. In the generic case, we characterize the analytic partially integrable systems by using orbitally equivalent normal forms. We also solve the problem through the existence of a class of formal inverse Jacobi multiplier of the system.engAtribución-NoComercial-SinDerivadas 3.0 Españahttp://creativecommons.org/licenses/by-nc-nd/3.0/es/journal article10.1017/prm.2022.19open access12 Matemáticas