Abstract
In this paper, we numerically investigated the dynamical evolution of the Bianchi IX Universe in the presence of inflation caused by a self-interacting scalar field. To find traces of chaos in the system, we calculate basin diagrams using the grid method and the smaller alignment index (SALI) method. The final states obtained with the SALI method have been rescaled, aiming to have the same number of final states of the grid method. This assumption allows us to directly compare the basin diagrams obtained with both methods, which exhibit very similar patterns. The fractality of the basins is then determined by means of two indicators: the boundary basin entropy and the smallest box-counting dimension. Our results indicate that in the presence of inflation, the fractal structures tend to disappear in the basin diagrams, and therefore, the suppression of chaos in the inflationary Bianchi IX cosmology is possible.