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The sensitivity of the trajectories of the stars to small changes (perturbations) on the initial conditions was first reported by Miller [2]. The improved computational power now available allowed a sistematic study of the typical time scale of this instability in terms of the characteristic crossing time of the system [3].

In this work we present results obtained from numerical integration of the N-body gravitational problem and the associated variational equations of motion, using the NNEWTON package [4]. We use the ``Lyapunov Characteristic Indicator'' [5] to estimate the time scale of the instability associated with the exponential growth of perturbations (variations) on the initial conditions.

Our preliminary results are in good agreement with those of [6] and show a simple relation between the time scale of the instability, the number of particles and the crossing time of the system.

**References :**

- [1]
- Poincare, H. (1892): Les Methodes Nouvelles de la Mecanique Celeste. Gauthier-Villars, Paris, Vol. (I).
- [2]
- Miller, R. H. (1964): Irreversibility in Small Stellar Dynamics Systems. Astrophysical Journal, 140, 250.
- [3]
- Kandrup, H. E. (1994): Chaos, Regularity, and Noise in Self-Gravitating Systems. An invited plenary talk at: The Seventh Marcel Grossmann Meeting.
- [4]
- [4] Pereira, N. S. A. (2001): Master's Thesis. Faculty of Sciences, University of Lisbon, Portugal.
- [5]
- Heggie, D. C. (1991): Chaos in the N-Body Problem of Stellar Dynamics. Predictability, Stability, and Chaos in N-Body Dynamical Systems, Edited by A. E. Roy, Plenum Press, New York.
- [6]
- Goodman, J., Heggie, D. C., Hut, P. (1993): On the Exponential Instability of N-Body Systems. The Astrophysical Journal, 415:715-733.