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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Mather, J. N., Existence of quasiperiodic orbit for twist homeomorphisms of the annulus,Topology, 1982, 21: 457.
Aubry, S., LeDaeron, P. Y., The discrete Frenkel Kontorova model and its application,Physica, 1983, 8D: 381.
Denzler, J., Mather sets for plane Hamiltonian systems,ZAMP, 1987, 38: 791.
Jiang, M. Y., Pei, M. L., Mather sets for superlinear plane Hamiltonian systems,Dynamic Systems and Applications, 1993, 2: 189.
Pei, M. L., Mather sets for superlinear Duffing equations,Science in China, Ser. A, 1993, 36: 524.
Pei, M. L., Mather sets for finite twist maps of a cylinder and semilinear Duffing equations,J. Diff. Equa., 1994, 113: 106.
Mather, J. N., Action minimizing invariant measures for positive definite Lagrangian systems,Math. Z., 1991, 207: 169.
Moser, J., Recent developments in the theory of Hamiltonian systems,SI AM Review, 1986, 28: 459.
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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