Let with h analytic of small norm. The problem of Arnold's diffusion consists in finding conditions on h which guarantee the existence of orbits Q of with connecting two arbitrary points of frequency space. Recently, J. N. Mather has found a sufficient condition for Arnold's diffusion; this condition is not read on h itself, but on the set of all action-minimizing orbits of . In this paper we try to characterize those action-minimizing orbits whose mean frequency is close to periodic.
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U. Bessi, V. Semijopuva, Minimal orbits close to periodic frequencies. Comment. Math. Helv. 73 (1998), no. 4, pp. 516–547