Astronomy and Astrophysics – Astrophysics – High Energy Astrophysical Phenomena
Scientific paper
2010-11-11
MATHEMATICS AND ASTRONOMY: A JOINT LONG JOURNEY: Proceedings of the International Conference. AIP Conference Proceedings, Volu
Astronomy and Astrophysics
Astrophysics
High Energy Astrophysical Phenomena
10 pages, 10 figures, published
Scientific paper
10.1063/1.3506071
We study the motion of charged test particles around a Kerr black hole immersed in the asymptotically uniform magnetic field, concluding that off-equatorial stable orbits are allowed in this system. Being interested in dynamical properties of these astrophysically relevant orbits we employ rather novel approach based on the analysis of recurrences of the system to the vicinity of its previous states. We use recurrence plots (RPs) as a tool to visualize recurrences of the trajectory in the phase space. Construction of RPs is simple and straightforward regardless of the dimension of the phase space, which is a major advantage of this approach when compared to the "traditional" methods of the numerical analysis of dynamical systems (for instance the visual survey of Poincar\'{e} surfaces of section, evaluation of the Lyapunov spectra etc.). We show that RPs and their quantitative measures (obtained from recurrence quantification analysis -- RQA) are powerful tools to detect dynamical regime of motion (regular vs. chaotic) and precisely locate the transitions between these regimes.
Karas Vladimir
Kopacek Ondrej
Kovar Jiri
Stuchlik Zdenek
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