Geodesic
High degeneracy of effective Hamiltonian in two dimensions
Annales de l'I.H.P. Analyse non linéaire, Tome 39 (2022) no. 1, pp. 201-223

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Consider the effective Hamiltonian H ¯(p) associated with the mechanical Hamiltonian H(p,x)=1 2|p| 2 +V(x). We prove that for generic V, H ¯ is piecewise one-dimensional in a dense open set in two dimensions using Aubry–Mather theory.

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DOI : 10.4171/aihpc/6
Classification : 35B27, 35F20, 37J51 
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     author = {Yu, Yifeng},
     title = {High degeneracy of effective {Hamiltonian} in two dimensions},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {201--223},
     volume = {39},
     number = {1},
     year = {2022},
     doi = {10.4171/aihpc/6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpc/6/}
}
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Yu, Yifeng. High degeneracy of effective Hamiltonian in two dimensions. Annales de l'I.H.P. Analyse non linéaire, Tome 39 (2022) no. 1, pp. 201-223. doi: 10.4171/aihpc/6

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