Variational approach to Arnold diffusion. (English) Zbl 1427.37049
Summary: Arnold diffusion was conjectured by V. I. Arnol’d [Sov. Math., Dokl. 5, 581–585 (1964; Zbl 0135.42602); translation from Dokl. Akad. Nauk SSSR 156, 9–12 (1964)]
as a typical phenomena of topological instability in classical mechanics. In this paper, we give a panorama of the researches on Arnold diffusion using the variational approaches.
MSC:
| 37J40 | Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion |
| 37J51 | Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods |
| 49L25 | Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games |
Citations:
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