报告题目：Resonance conjecture with the constraint of controlled Markov diffusion via weak KAM theory

报告人：牛勋 东北师范大学数学与统计学院

报告时间： 2025年11月20日14:30 – 15:30

报告地点：正新楼 105

校内联系人：张赫[email protected]

报告摘要 In this talk, we investigates resonance in nearly integrable Hamiltonian systems under the constraint of controlled Markov diffusion, using the framework of weak KAM theory. We demonstrate that the Hamilton-Jacobi equation associated with such systems admits at least m_0 + 1 weak KAM solutions at relative equilibria, where m_0 represents the multiplicity of the resonant surface. These weak KAM solutions enable the transformation of nearly integrable Hamiltonian systems into a class of integrable Hamiltonian systems under stationary states.

报告人简介：牛勋，东北师范大学数学与统计学院预聘副研究员，主要研究哈密顿动力系统;在. J. Math. Pures Appl. ，Sci. China Math. ， J. Differential Equations等高水平杂志上发表多篇论文，获得国家自然科学基金青年科学基金项目（C类）。