Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	韦屏远博士,北京国际数学研究中心
Inviter:
Title:	A Brief Introduction to Stochastic Hamiltonian Systems on Jacobi Manifold
Language:	Chinese
Time & Venue:	2023.07.12 15:00-16:00 南楼N913
Abstract:	The generalization of classical geometric mechanics (including the study of symmetries, Hamiltonian and Lagrangian mechanics, and the Hamilton-Jacobi theory, etc.) to the context of stochastic dynamics has drawn more and more attention in recent decades. In this talk, we generalize the systems of Hamiltonian diffusions, which were introduced and studied by Bismut, to accommodate arbitrary Jacobi manifolds as phase spaces and general continuous semimartingales as forcing noises. We show that such systems preserve characteristic structures and develop a stochastic version of Hamilton–Jacobi theory. (We remake that both Jacobi and Poisson manifolds were introduced by Lichnerowicz. Jacobi ones are regarded as the natural generalization of Poisson ones and in particular of symplectic, cosymplectic and Lie–Poisson structures. However, very interesting manifolds like contact manifolds and locally conformal symplectic manifolds are also Jacobi and they are not Poisson.)