周渊，北京师范大学

For the classical N-body problem, Maderna-Venturelli [Ann. Math. 2020] proved the existence of hyperbolic motions with any positive energy constant, starting from any configuration and along any noncollision configuration. Their original proof relies on the long time behavior of solutions by Chazy 1922 and Marchal-Saari 1976, on the Holder estimate for Mane's potential by Maderna 2012, and on the weak KAM theory. In this lecture, we give a new and completely different proof for the above existence of hyperbolic motions. This is a joint work of Jiayin Liu, Duokui Yan and Yuan Zhou.