Topological and control theoretic properties of Hamilton-Jacobi equations via Lax-Oleinik commutators

Piermarco Cannarsa, Wei Cheng, Jiahui Hong

In the context of weak KAM theory, we discuss the commutators $\{T_t^{-}\circ T_t^{+}{\}}_{t⩾0}$ and $\{T_t^{+}\circ T_t^{-}{\}}_{t⩾0}$ of Lax-Oleinik operators. We characteriz…