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On a theorem by Mather and Aubry-Mather sets for planar Hamiltonian systems

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Abstract

A result due to Mather on the existence of Aubry-Mather sets for superlinear positive definite Lagrangian systems is generalized in one-dimensional case. Applications to existence of Aubry-Mather sets of planar Hamiltonian systems are given.

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Project supported by the National Natural Science Foundation of China (Grant No. 19631020).

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Jiang, M. On a theorem by Mather and Aubry-Mather sets for planar Hamiltonian systems. Sci. China Ser. A-Math. 42, 1121–1128 (1999). https://doi.org/10.1007/BF02875979

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  • DOI: https://doi.org/10.1007/BF02875979

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