Abstract: The study of group actions and the behaviour of orbits can be utilized to understand Diophantine approximations. We will focus on the dynamical equivalent to vectors with 'infinitely good' diophantine approximation. From the dynamical point of view, Weiss conjectured a complete classification of the relevant trajectories. We will discuss the steps and different tools used in proving the last piece of this conjecture. This is a joint work with Omri Solan.


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