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The convergence of Lax-Oleinik semigroup for time-periodic Lagrangian

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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 F c ((x, s), (x′, s′ +T n )), the convergence of which is closely related to the Lax-Oleinik semigroup.

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  1. School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou, 215009, China

    Xia Li

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  1. Xia Li
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Correspondence to Xia Li.

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Li, X. The convergence of Lax-Oleinik semigroup for time-periodic Lagrangian. Sci. China Math. 57, 343–352 (2014). https://doi.org/10.1007/s11425-013-4649-2

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  • DOI: https://doi.org/10.1007/s11425-013-4649-2

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