Bifurcations and Chaos in Ho\v{r}ava-Lifshitz Cosmology

The nature of generic spacelike singularities in general relativity is connected with first principles, notably Lorentzian causal structure, scale invariance and general covariance. To bring a new perspective on how these principles affect generic spacelike singularities, we consider the initial singularity in spatially homogeneous Bianchi type VIII and IX vacuum models in Ho\v{r}ava-Lifshitz gravity, where relativistic first principles are replaced with anisotropic scalings of Lifshitz type. Within this class of models, General Relativity is shown to be a bifurcation where chaos becomes generic. To describe the chaotic features of generic singularities in Ho\v{r}ava-Lifshitz cosmology, we introduce symbolic dynamics within Cantor sets and iterated function systems.