The Minkowski continued fraction algorithm from a dynamics perspective

The Littlewood Conjecture is an open problem in simultaneous Diophantine approximation. It and the stronger Margulis Conjecture, a proof of which would imply Littlewood, are currently viewed using dynamic systems. In this paper we will look at the space o f ''triple points" , also known as the domain for the Minkowski continued fraction algorithm, using a dynamics perspective. We will look at ''maximal boxes" and associated ''uniquely" maximal systole cubes with their related lattice configurations from different perspectives. We will explore possible indexes for these related lattices. This will be done to attempt to shed some light on the configuration space of triple points.