Stochastic Time-Periodic Tonelli Lagrangian on Compact Manifold

2020/09/21 by Liang Chen, Chen, Liang
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2009.09834

openalex publication_date 2020/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study a class of time-periodic stochastic Tonelli Lagrangians on compact manifolds. Precisely, we discuss the stochastic Mane Critical Value, prove the existence of stochastic Weak KAM solutions of the related Hamilton-Jacobi equation. Furthermore, we survey the global minimizer.

Citations

• Action minimizing invariant measures for positive definite Lagrangian systems
• Weak solutions of the Hamilton-Jacobi equation for time periodic lagrangians

Related

• Periodic limit for non-autonomous Lagrangian systems and applications to a Kuramoto type model
• Weak KAM Theory topics in the stationary ergodic setting
• Stochastic Hamiltonian dynamical systems
• Weak solutions of the Hamilton-Jacobi equation for time periodic lagrangians
• Weak KAM theory for subriemannian Lagrangians