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arXiv · 1409.8520

Homoclinic orbits and critical points of barrier functions

Piermarco Cannarsa·Wei Cheng
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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 $\mathbb{T}^n$. We also prove a critical point theorem for barrier functions, and the existence of such homoclinic orbits on $\mathbb{T}^2$ as an application.

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Piermarco Cannarsa, Wei Cheng. 2014-09-30. Homoclinic orbits and critical points of barrier functions. https://doi.org/10.1088/0951-7715%2F28%2F6%2F1823

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