Periodic orbits and Arnold diffusion (Q1865969)

The authors consider three degrees of freedom initially hyperbolic Hamiltonian systems \(H_{\mu}\) with perturbation parameter \(\mu\ll 1.\) Under certain technical assumptions it is shown that the Arnold diffusion time can be of order \(\frac{1}{\mu}\log (\frac{1}{\mu})\) as conjectured by \textit{P. Lochak} [NATO ASI Ser., Ser. C, Math, Phys. Sci. 533, 168-183 (1999; Zbl 0986.37054)]. A dual chain of hyperbolic periodic orbits surrounding a given transition chain of partially hyperbolic tori is constructed. The authors use Easton's method of windows to give a general formula for the time of drift along such a chain of hyperbolic periodic orbits, from which the main result follows.