Seminarium Teorii Względności i Grawitacji

In this talk I will give a broad outline of recent progress concerning analytical and numerical progress as regards oscillatory singularities in inhomogeneous cosmology in general relativity. In particular I will focus on the relationship and differences between the usual BKL scenario and so-called recurring spike formation, which is needed in order to form a complete picture of generic asymptotic oscillatory dynamics. I also discuss the character and underlying physical reasons for the hierarchical state space structure that is essential for understanding both types of behaviour, and why this structure hints at the existence of hidden asymptotic symmetries. In addition I comment on relationships between different methods such as dynamical systems methods and Hamiltionian billiards. Finally, I conclude with some speculations and point at some open issues, which will hopefully be helpful for possible future investigations.