Local instability of Bianchi IX dynamics in the first BKL approximation

The generalized criterion of the local instability from the geodesic deviation equation is demonstrated. We show that in the first BKL approximation of the Bianchi IX model the singularity of the inverse Jacobi metric or the Ricci scalar does not mean the corresponding singularity in the geodesic deviation equation. We also calculate the characteristic Lyapunov time for the chaotic B(IX) dynamics.