The paper uses Rabinowitz-Stredulinsky minimization to construct heteroclinic solutions (one or two directions) and more complex minimal Birkhoff solutions for rational rotation vectors in a generalized Frenkel-Kontorova model when adjacent periodic configurations exist.
Bangert, The existence of gaps in minimal foliations , Aequationes Mathematicae 34.2 (1987): 153-166
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Heteroclinic solutions for a generalized Frenkel-Kontorova model by minimization methods of Rabinowitz and Stredulinsky
The paper uses Rabinowitz-Stredulinsky minimization to construct heteroclinic solutions (one or two directions) and more complex minimal Birkhoff solutions for rational rotation vectors in a generalized Frenkel-Kontorova model when adjacent periodic configurations exist.