The fractal nature of the power spectrum as an indicator of chaos in the Bianchi-IX cosmological model

Using two different methods, we compute the fractal dimension of the power spectrum associated with numerical solutions of the spatially homogeneous Bianchi IX cosmological model in Misner-Chitre coordinates. According to Perdang's criterion, the noninteger character of this dimension is reflection of chaos and can be used to measure it, in the same spirit as the Lyapunov exponent of the Kolmogorov entropy. The results obtained indicate the chaotic nature of the behaviour of the Bianchi IX model near the cosmological singularity.