Affiliation:
1. Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Paseo del Bosque s/n, 1900 La Plata, Argentina
2. Instituto de Astrofísica de La Plata – UNLP-Conicet, Paseo del Bosque s/n, 1900 La Plata, Argentina
Abstract
ABSTRACT
We show that the Lyapunov exponents of a periodic orbit can be easily obtained from the eigenvalues of the monodromy matrix. It turns out that the Lyapunov exponents of simply stable periodic orbits are all zero, simply unstable periodic orbits have only one positive Lyapunov exponent, doubly unstable periodic orbits have two different positive Lyapunov exponents, and the two positive Lyapunov exponents of complex unstable periodic orbits are equal. We present a numerical example for periodic orbits in a realistic galactic potential. Moreover, the centre manifold theorem allowed us to show that stable, simply unstable, and doubly unstable periodic orbits are the mothers of families of, respectively, regular, partially, and fully chaotic orbits in their neighbourhood.
Funder
Universidad Nacional de La Plata
Consejo Nacional de Investigaciones Científicas y Técnicas
Publisher
Oxford University Press (OUP)
Subject
Space and Planetary Science,Astronomy and Astrophysics
Cited by
2 articles.
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