Accelerator modes and anomalous diffusion in 3D volume-preserving maps

James D. Meiss; Narcís Miguel; Carles Simó; Arturo Vieiro

doi:10.1088/1361-6544/aae69f

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arXiv · 1802.10484

Accelerator modes and anomalous diffusion in 3D volume-preserving maps

James D. Meiss·Narcís Miguel·Carles Simó·Arturo Vieiro

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Abstract

Angle-action maps that are periodic in the action direction can have accelerator modes: orbits that are periodic when projected onto the torus, but that lift to unbounded orbits in an action variable. In this paper we construct a volume-preserving family of maps, with two angles and one action, that have accelerator modes created at Hopf-one (or saddle-center-Hopf) bifurcations. Near such a bifurcation we show that there is often a bubble of invariant tori. Computations of chaotic orbits near such a bubble show that the trapping times have an algebraic decay similar to that seen around stability islands in area-preserving maps. As in the 2D case, this gives rise to anomalous diffusive properties of the action in our 3D map.

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James D. Meiss, Narcís Miguel, Carles Simó, Arturo Vieiro. 2018-02-28. Accelerator modes and anomalous diffusion in 3D volume-preserving maps. https://doi.org/10.1088/1361-6544%2Faae69f

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