Abstract
We study a class of weakly coupled systems of Hamilton–Jacobi equations using the random frame introduced in [H. Mitake, A. Siconolfi, H. V. Tran and N. Yamada, A Lagrangian approach to weakly coupled Hamilton–Jacobi systems, SIAM J. Math. Anal. 48(2) (2016) 821–846; doi: https://doi.org/10.1137/15M1010841 ]. We provide a cycle condition characterizing the points of Aubry set. This generalizes a property already known in the scalar case.
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