Lyapunov exponents at a fixed point

I am trying to find the Lyapunov exponents at a fixed point as given in the paper here(page 14). The code that I have used till now is given below:

K1 = 6.90; K2 = 16.05; K3 = 9.65; K4 = 3.27; K5 = 6.55;
\[Omega]sq[0] = -0.923; \[Omega]sq[1] = 6.478;
lagrangian =
Sum[c[n]'[t]^2 - c[n][t]^2 \[Omega]sq[n], {n, {0, 1}}] +
K1 c[0][t]^3 + K2 c[0][t] c[1][t]^2 + K3 c[0][t] c[0]'[t]^2 +
K4 c[0][t] c[1]'[t]^2 + K5 c[0]'[t] c[1][t] c[1]'[t];
c[0][t_] := OverTilde[c][0][t] + \[Alpha]1*OverTilde[c][0][t]^2 + \[Alpha]2*OverTilde[c][1][t]^2;
c[1][t_] := OverTilde[c][1][t] + \[Alpha]3*OverTilde[c][0][t]*OverTilde[c][1][t];
\[Alpha]1 = -2; \[Alpha]2 = -0.5; \[Alpha]3 = -1;
n = Expand[lagrangian];
vars = {OverTilde[c][0][t], OverTilde[c][1][t],
Derivative[1][OverTilde[c][0]][t],
Derivative[1][OverTilde[c][1]][t]};
lagrangian =
Normal[Series[n /. Thread[vars -> m*vars], {m, 0, 3}]] /. m -> 1;
momentum[n_] := D[lagrangian, Derivative[1][OverTilde[c][n]][t]]
hamiltonian = Expand[Sum[momentum[n]*Derivative[1][OverTilde[c][n]][t], {n, {0, 1}}] - lagrangian];
eulerLagrange[lagrangian_, vars_, dvars_] :=
Thread[Table[D[D[lagrangian, dvar], t], {dvar, dvars}] - Table[D[lagrangian, var], {var, vars}] ==
ConstantArray[0, Length[vars]]];
equationsOfMotion = eulerLagrange[lagrangian, {OverTilde[c][0][t], OverTilde[c][1][t]},
{Derivative[1][OverTilde[c][0]][t], Derivative[1][OverTilde[c][1]][t]}]


2. Once you have the vector F(x), you can calculate its Jacobian in mathematica with the function: jacobianMatrix[f_List, x_List] := Outer[D, f, x], e.g.
j=jacobianMatrix[f, {c1,c2,c3,c4}] (or however you want to name your variables)
3. For the dynamics of a local fixed point, the Lyapunov exponents are just the eigenvalues of the fixed point. You will first need to find the fixed point location via something like fp = NSolve[f==0,{c1,c2,c3,c4}]. Then plug the fixed point location into your jacobian matrix j/.fp and finally calculate its eigenvalues with eigenvalues = Eigenvalues[j/.fp].