Given a nonlinear four dimensional system of ODEs, I have found the fixed point and linearized to acquire the Jacobian. I am beginning to calculate the eigenvalues of the Jacobian from the quartic characteristic polynomial.
The Jacobian's elements consist of functions that are not specified, for example $F(x,y)$ and $F_x(x,y)$. Also, $C_\infty$ differentiability is assumed. I do not want to use numerical analysis.
References would be useful--typically textbooks analyse two dimensional systems qualitatively, but do not go higher, which suggests to me I am taking an unconventional approach.
Should I be using a symbolic manipulation computer package?