The study of the motion law of N particles under universal gravitation in the N-body problem is a simplified mathematical model for describing the motion of celestial bodies and an important source for the birth of mathematical theories. In this speech, we will introduce some important issues and latest developments regarding the periodic orbits of N-body problems.

Speaker Biography: Hu Xijun, Professor and Executive Vice Dean of the School of Mathematics at Shandong University, recipient of the National Outstanding Youth Fund. My main research areas are Hamiltonian systems and nonlinear analysis. Significant progress has been made in the research of the following issues: 1 Several new research methods have been established in the study of the stability of periodic orbits in N-body problems, demonstrating the stability of several classical orbits such as Lagrangian orbits and "8" - shaped orbits; 2. Established the index theory of Hamiltonian systems with same and different orbits and applied it to the study of odd orbits and wave solutions in a class of reaction-diffusion equations in N-body problems; three In the study of Hamiltonian operators, the Hill type formula and trace formula have been developed and perfected, providing the first quantitative characterization of the stability of periodic orbits.