"Dynamical friction as collective many-body interactions": Dynamical friction is drag force on a massive particles, which is caused by a myriad of less massive ambient particles. The essence of this friction force is the superposition of collision-less gravity interactions between them, and dynamical friction is a general phenomenon in various astronomical objects, such as galaxies in a cluster of galaxies, star clusters in a galaxy and planets in a proto-planetary disc. An analytic solution of dynamical friction has already been invented by Chandrasekhar (1943) and well-known as the Chandrasekhar formula. However, is has also long been known that the Chandrasekhar formula becomes inaccurate in a spherical system with a constant density (cored region). In the cored region, the formula predicts orbital shrinkage of a massive particle and that the particles would have fallen into the centre of the system. On the other hand, N-body simulations have shown that dynamical friction does not work in such a cored region and the massive particle can keep orbiting around the centre. In this talk, I will be discussing why dynamical friction ceases in the cored density and why the Chandrasekhar formula fails to predict the orbital evolution. I will show results of my N-body simulations and detailed analyses of behaviours of interacting particles. As a result, I will indicate that the nature of dynamical friction is the collective effect of many-body interactions rather than two-body interactions, the stalling of dynamical friction is due to non-linear behaviours of ambient particles that is different from when the massive particle is outside the cored region.