1:2 resonance for reversible vector fields (Q1598501)

The author deals with the \(1:2\) resonance for reversible vector fields in \(\mathbb{R}^4\) depending on a parameter \(\mu: dX/dt= F(X,\mu),\) where \(F\) is in \(C^k\), \(F(0,\mu)=0\) and \(D_X F(0,0)\) has two pairs of simple eigenvalues \(+ i\omega_1, -i\omega_1, +i\omega_2\) and \(-i\omega_2\), and there exists a symmetry \(S\) such that \(SF(X,\mu)=-F(SX,\mu)\).