Year: 2018
Type: article
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.
Source: Nonlinearity
Authors: James D Meiss, Narcís Miguel, Carles Simó, Arturo Vieiro
Institutions: University of Colorado Boulder, Universitat de Barcelona
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2788247192