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2018-11-15

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/192805

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

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https://doi.org/10.1088/1361-6544/aae69f

Abstract

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.

Subject

Teoria de la bifurcació, Sistemes dinàmics diferenciables, Equacions diferencials ordinàries, Sistemes dinàmics de baixa dimensió, Processos de Markov

Subject (English)

Bifurcation theory, Differentiable dynamical systems, Ordinary differential equations, Low-dimensional dynamical systems, Markov processes

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Citation

MEISS, James D., et al. Accelerator modes and anomalous diffusion in 3D volume-preserving maps. Nonlinearity. 2018. Vol. 31, num. 12, pags. 5615-5642. ISSN 0951-7715. [consulted: 13 of June of 2026]. Available at: https://hdl.handle.net/2445/192805

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