In this talk, we examine a two-parameter family of skew product systems featuring two invariant subspaces, each supporting a distinct chaotic attractor. Within an open region of the parameter plane, we observe that the corresponding basins of attraction are intermingled-meaning every neighborhood of a point in one basin contains points from the other with positive measure. This phenomenon reflects strong sensitivity to initial conditions and poses significant challenges for predictability. The basins are separated by a fractal boundary curve, whose intricate geometry we analyze both visually and quantitatively. We compute the stability index, which quantifies the likelihood of nearby points converging to different attractors. Using thermodynamic formalism, we study the statistical behavior of this index and perform a multifractal analysis of its level sets. This analysis reveals a spectrum of dimensions characterizing the fine-scale structure of the basin boundaries. The multifractal properties of the stabilty index offer a powerful framework for classifying basin complexity and for understanding how small perturbations can lead to dramatically different long-term behaviors.

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