On the Integrability Problem for the Hopf-Zero singularity and its relation with the inverse Jacobi multiplier

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1909.04398.pdf (244.57 KB)

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2021

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Ciencias Integradas

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Center

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http://hdl.handle.net/10272/20808

DOI

10.1016/j.amc.2021.126241

Abstract

In this paper we use the orbital normal form of the nondegenerate Hopf-zero singularity to obtain necessary conditions for the existence of first integrals for such singularity. Also, we analyze the relation between the existence of first integrals and of inverse Jacobi multipliers. Some algorithmic procedures for determining the existence of first integrals are presented, and they are applied to some families of vector fields.

Keywords

Integrability problem; Nondegenerate Hopf-zero singularity; Quasi-homogeneous normal forms; Analytic first integrals; lnverse Jacobi multipliers

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12 Matemáticas

Bibliographic citation

Algaba, A., Fuentes, N., Gamero, E., & García, C. (2021). On the integrability problem for the Hopf-zero singularity and its relation with the inverse Jacobi multiplier. In Applied Mathematics and Computation (Vol. 405, p. 126241). Elsevier BV. https://doi.org/10.1016/j.amc.2021.126241

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