Twin vector fields

This is a SageMath code used to compute twin vector fields. These computations follow the ideas presented in the following paper:

• Ramirez, V. Twin vector fields and independence of spectra for quadratic vector fields. J. Dynam. Control Syst. 23 (2017), no. 3, 623–633.

DOI: 10.1007/s10883-016-9344-5, arXiv: 1508.02413

The theorem in question

We work with quadratic vector fields

P(x,y)\frac{\partial}{\partial x} + Q(x,y)\frac{\partial}{\partial y}

on \mathbb{C}^2 having isolated singularities.

Definition: We say that two vector fields v and v' are twin vector fields if they have the same singular set, and for each singular point they the linearization matrices have the same eigenvalues.

Theorem: A generic quadratic vector field has exactly one twin.