Abstract: 

Let $G$ be a definably amenable groups over $p$-adics. We study the definable topological dynamics $(G, S_G(\mathbb{Q}_p))$ of $G$ acting on its type space. We focus on the question of whether weakly generic types coincide with almost periodic types which was raised by Newelski and then restarted by Chernikov and Simon on NIP definably amenable groups. 

We show that the stationarity is a sufficient and necessary condition for the positive answer of the question. This is a joint work with Ningyuan Yao.