Examples of Aubry sets. (English) Zbl 1090.37047
Towards so far unpublished results concerning orbits in certain Langrangian systems, the author considers so-called Aubry qoutient sets, introduced in [Commun. Pure Appl. Math. 56, 1178–1183 (2003; Zbl 1046.37039)] by the author, which help to construct orbits by minimization in case of time-periodic Lagrangians. The main result provides examples for Lagrangians with quotient Aubry sets that are isometric to a closed interval. In addition, the author gives an example for which the Aubry set is not upper-semicontinuous in the Lagrangian.
Reviewer: Jens Rademacher (Berlin)
MSC:
37J50 | Action-minimizing orbits and measures (MSC2010) |
37J40 | Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion |