Existence of infinitely many homoclinic orbits to Aubry sets for positive definite Lagrangian systems |
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Authors: | Xiaojun Cui Chong-Qing Cheng Wei Cheng |
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Institution: | Department of Mathematics, Nanjing University, Hankou Road 22, Nanjing, Jiangsu 210093, P.R.China |
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Abstract: | In this paper, we study the problem of homoclinic orbits to Aubry sets for time-periodic positive definite Lagrangian systems. We show that there are infinitely many homoclinic orbits to some Aubry set under the conditions that the associated Mather set is uniquely ergodic and the first relative homology group of the projection of this Aubry set is nonzero. |
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Keywords: | Lagrangian system Aubry set Homoclinic orbit |
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