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 $\mathbbT^n$. We also prove a critical point theorem for barrier functions, and the existence of such homoclinic orbits on $\mathbbT^2$ as an application.
Cannarsa, P., Cheng, W. (2015). Homoclinic orbits and critical points of barrier functions. NONLINEARITY, 28(6), 1823-1840 [10.1088/0951-7715/28/6/1823].
Homoclinic orbits and critical points of barrier functions
CANNARSA, PIERMARCO;
2015-01-01
Abstract
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 $\mathbbT^n$. We also prove a critical point theorem for barrier functions, and the existence of such homoclinic orbits on $\mathbbT^2$ as an application.File in questo prodotto:
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