Astron. Astrophys. Suppl. Ser. 147, 205-228
P.M. Cincotta1 - C. Simó2
Send offprint request: P.M. Cincotta
1 - Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Paseo del Bosque, 1900 La Plata, Argentina
2 - Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
Received July 30, 1999; accepted September 4, 2000
In a second part we introduce a new indicator of the basic dynamics, the Mean Exponential Growth factor of Nearby Orbits (MEGNO), that is suitable to investigate the phase space structure associated to a general Hamiltonian. When applied to the 2D logarithmic potential it is shown to be effective to obtain a picture of the global dynamics and, also, to derive good estimates of the largest Lyapunov characteristic number in realistic physical times. Comparisons with other techniques reveal that the MEGNO provides more information about the dynamics in the phase space than other wide used tools.
Finally, we discuss the structure of the phase space associated to the 2D logarithmic potential for several values of the semiaxis ratio and energy. We focus our attention on the stability analysis of the principal periodic orbits and on the chaotic component. We obtain critical energy values for which connections between the main stochastic zones take place. In any case, the whole chaotic domain appears to be always confined to narrow filaments, with a Lyapunov time about three characteristic periods.
Key words: galaxies: dynamics -- stellar dynamics -- methods: analytical-numerical -- chaos
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