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An example of Arnold diffusion for near-integrable Hamiltonians. (English) Zbl 1141.70009
Summary: Using the ideas of U. Bessi [Nonlinear Anal., Theory Methods Appl. 26, No. 6, 1115–1135 (1996; Zbl 0867.70013)] and J. Mather [J. Graduate Class 2001–2002. Princeton (2002)], we present a simple mechanical system exhibiting Arnold diffusion. This system of a particle in a small periodic potential can be also interpreted as ray propagation in a periodic optical medium with a near-constant index of refraction. Arnold diffusion in this context manifests itself as an arbitrary finite change of direction for nearly constant index of refraction.

MSC:
70H08 Nearly integrable Hamiltonian systems, KAM theory
78A05 Geometric optics
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