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Accelerator modes and anomalous diffusion in 3D volume-preserving maps
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Angle-action maps that have a periodicity 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 family of volume-preserving 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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MEISS, James d., MIGUEL I BAÑOS, Narcís, SIMÓ, Carles, VIEIRO YANES, Arturo. Accelerator modes and anomalous diffusion in 3D volume-preserving maps. _Nonlinearity_. 2018. Vol. 31, núm. 12, pàgs. 5615-5642. [consulta: 23 de gener de 2026]. ISSN: 0951-7715. [Disponible a: https://hdl.handle.net/2445/192805]