Homoclinic orbits and critical points of barrier functions

Piermarco Cannarsa, Wei Cheng
2015 Nonlinearity  
We interpret the close link between the critical points of Mather's barrier functions and minimal homoclinic orbits with respect to the Aubry sets on $\mathbb{T}^n$. We also prove a critical point theorem for barrier functions, and the existence of such homoclinic orbits on $\mathbb{T}^2$ as an application.
doi:10.1088/0951-7715/28/6/1823 fatcat:oetme4jqsrh7zptjtpoe2qa5li