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http://hdl.handle.net/2445/192805
Title: | Accelerator modes and anomalous diffusion in 3D volume-preserving maps |
Author: | Meiss, James D. Miguel i Baños, Narcís Simó, Carles Vieiro Yanes, Arturo |
Keywords: | Teoria de la bifurcació Sistemes dinàmics diferenciables Equacions diferencials ordinàries Sistemes dinàmics de baixa dimensió Processos de Markov Bifurcation theory Differentiable dynamical systems Ordinary differential equations Low-dimensional dynamical systems Markov processes |
Issue Date: | 15-Nov-2018 |
Publisher: | IOP Publishing |
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. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1088/1361-6544/aae69f |
It is part of: | Nonlinearity, 2018, vol. 31, num. 12, p. 5615-5642 |
URI: | http://hdl.handle.net/2445/192805 |
Related resource: | https://doi.org/10.1088/1361-6544/aae69f |
ISSN: | 0951-7715 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
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682405.pdf | 6.36 MB | Adobe PDF | View/Open |
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