The Relative Lyapunov Indicator: An Efficient Method of Chaos Detection

Authors: Sándor, Zsolt¹; Érdi, Bálint²; Széll, András³; Funk, Barbara⁴

Source: Celestial Mechanics and Dynamical Astronomy, Volume 90, Numbers 1-2, September 2004 , pp. 127-138(12)

Publisher: Springer

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Abstract:

A recently introduced chaos detection method, the relative Lyapunov indicator (RLI) is investigated in the cases of symplectic mappings and of a continuous Hamiltonian system. It is shown that the RLI is an efficient and easy-to-calculate numerical tool in determining the true nature of individual orbits, and in separating ordered and regular regions of the phase space of dynamical systems. An application of the RLI for stability investigations of some recently discovered exoplanetary systems is also presented.

Keywords: chaos detection; exoplanetary systems; Lyapunov indicators

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10569-004-8129-4

Affiliations: 1: Department of Astronomy, 011011011011011011011011Eötvös University H-1117 Budapest, Pázmány Péter sétány 1/A, 011011011011011011011011011Hungary, Email: zs.sandor@astro.elte.hu 2: Department of Astronomy, 011011011011011011011011Eötvös University H-1117 Budapest, Pázmány Péter sétány 1/A, 011011011011011011011011011Hungary, , 3: School of Computing and Mathematical Sciences, 011011011011011011011011Glasgow Caledonian University, Cowcaddens Road, Glasgow G40BA, 011011011011011011011011011U.K, 4: Institute for Astronomy, 011011011011011011011011University of Vienna, 17 Türkenschanzstrasse, 011011011011011011011011011Vienna, 011011011011011011011011011Austria,

Publication date: 2004-09-01