Abstract
In this article, the convergence of so-called Lax-Oleinik semigroup is studied for time-periodic Lagrangian systems when the degree of freedom is greater than 2. Under certain conditions, we show that the Lax-Oleinik semigroup converges if the rotation vector is completely irrational. Removing such conditions, we will give another kind of convergence of the sequence Fc((x, s), (x′, s′ +Tn)), the convergence of which is closely related to the Lax-Oleinik semigroup.
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