Astronomy and Astrophysics – Astronomy
Scientific paper
Dec 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005pabei..23..318w&link_type=abstract
Progress in Astronomy (ISSN 1000-8349), Vol. 23, No. 4, p. 318 - 330 (2005)
Astronomy and Astrophysics
Astronomy
Celestial Mechanics, Chaos, Review, Orbit, Lyapunov Exponent, General Relativity
Scientific paper
In this paper we review in detail some methods for distinguishing between a regular orbit and a chaotic one in a Newtonian dynamical system, which contain Poincaré section, Lyapunov exponents, local Lyapunov exponents and their spectral distributions, fast Lyapunov exponent index, smaller alignment index, 0-1 test, frequency map analysis, and so on. In particular, merits, demerits and application of these diagnostic indexes are discussed. In principle, these indexes from the Newtonian frame can also be applied to relativistic gravitational systems in general. However, there may still exist some problems because they are not coordinate invariant. As a result, it is vital to understand the behavior of a relativistic gravitational system by a covariant way. For example, it is convenient to employ our way for the calculation of Lyapunov exponents with gauge invariance by use of the "1+3" splitting of a curved spacetime and the projected norm.
Huang Tian-Yi
Wu Xin
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