On the integrability problem for the Hopf-zero singularity and its relation with the inverse Jacobi multiplier

作者：

Highlights：

• The orbital normal form of the nondegenerate Hopf-zero singularity pro- vides necessary conditions for the existence offirst integrals for such singularity.

• The relation between the existence offirst integrals and of inverse Jacobi multipliers is analized.

• Some algorithmic procedures for determining the existence offirst inte- grals are presented.

摘要

•The orbital normal form of the nondegenerate Hopf-zero singularity pro- vides necessary conditions for the existence offirst integrals for such singularity.•The relation between the existence offirst integrals and of inverse Jacobi multipliers is analized.•Some algorithmic procedures for determining the existence offirst inte- grals are presented.

论文关键词：Integrability problem,Nondegenerate Hopf-zero singularity,Quasi-homogeneous normal forms,Analytic first integrals,Inverse Jacobi multipliers

论文评审过程：Received 14 September 2020, Revised 11 March 2021, Accepted 26 March 2021, Available online 13 April 2021, Version of Record 13 April 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126241