Journal article
Swetamber Das, Arnd Bäcker
Phys. Rev. E, vol. 101(3), American Physical Society, 2020 Mar, p. 032201
Phys. Rev. E, vol. 101(3), American Physical Society, 2020 Mar, p. 032201
Published version
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APA
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Das, S., & Bäcker, A. (2020). Power-law trapping in the volume-preserving Arnold-Beltrami-Childress map. Phys. Rev. E, 101(3), 032201. https://doi.org/10.1103/PhysRevE.101.032201
Chicago/Turabian
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Das, Swetamber, and Arnd Bäcker. “Power-Law Trapping in the Volume-Preserving Arnold-Beltrami-Childress Map.” Phys. Rev. E 101, no. 3 (March 2020): 032201.
MLA
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Das, Swetamber, and Arnd Bäcker. “Power-Law Trapping in the Volume-Preserving Arnold-Beltrami-Childress Map.” Phys. Rev. E, vol. 101, no. 3, American Physical Society, Mar. 2020, p. 032201, doi:10.1103/PhysRevE.101.032201.
BibTeX Click to copy
@article{das2020a,
title = {Power-law trapping in the volume-preserving Arnold-Beltrami-Childress map},
year = {2020},
month = mar,
issue = {3},
journal = {Phys. Rev. E},
pages = {032201},
publisher = {American Physical Society},
volume = {101},
doi = {10.1103/PhysRevE.101.032201},
author = {Das, Swetamber and Bäcker, Arnd},
month_numeric = {3}
}
Abstract
Understanding stickiness and power-law behavior of Poincaré recurrence statistics is an open problem for higher-dimensional systems, in contrast to the well-understood case of systems with two degrees of freedom. We study such intermittent behavior of chaotic orbits in three-dimensional volume-preserving maps using the example of the Arnold-Beltrami-Childress map. The map has a mixed phase space with a cylindrical regular region surrounded by a chaotic sea for the considered parameters. We observe a characteristic overall power-law decay of the cumulative Poincaré recurrence statistics with significant oscillations superimposed. This slow decay is caused by orbits which spend long times close to the surface of the regular region. Representing such long-trapped orbits in frequency space shows clear signatures of partial barriers and reveals that coupled resonances play an essential role. Using a small number of the most relevant resonances allows for classifying long-trapped orbits. From this the Poincaré recurrence statistics can be divided into different exponentially decaying contributions, which very accurately explains the overall power-law behavior including the oscillations.
Understanding stickiness and power-law behavior of Poincaré recurrence statistics is an open problem for higher-dimensional systems, in contrast to the well-understood case of systems with two degrees of freedom. We study such intermittent behavior of chaotic orbits in three-dimensional volume-preserving maps using the example of the Arnold-Beltrami-Childress map. The map has a mixed phase space with a cylindrical regular region surrounded by a chaotic sea for the considered parameters. We observe a characteristic overall power-law decay of the cumulative Poincaré recurrence statistics with significant oscillations superimposed. This slow decay is caused by orbits which spend long times close to the surface of the regular region. Representing such long-trapped orbits in frequency space shows clear signatures of partial barriers and reveals that coupled resonances play an essential role. Using a small number of the most relevant resonances allows for classifying long-trapped orbits. From this the Poincaré recurrence statistics can be divided into different exponentially decaying contributions, which very accurately explains the overall power-law behavior including the oscillations.
