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2013
Impact Factor

# Giancarlo Benettin

## Publications:

 Benettin G., Fasso F., Guzzo M. Long term stability of proper rotations and local chaotic motions in the perturbed Euler rigid body 2006, vol. 11, no. 1, pp.  1-17 Abstract The long term stability of the proper rotations of the perturbed Euler rigid body was recently investigated analytically in the framework of Nekhoroshev theory. In this paper we perform a parallel numerical investigation, with the double aim of illustrating the theory and to submit it to a critical test. We focus the attention on the case of resonant motions, for which the stability is not trivial (resonant proper rotations are indeed stable in spite of the presence of local chaotic motions, with positive Lyapunov exponent, around them). The numerical results indicate that the analytic results are essentially optimal, apart from a particular resonance, actually the lowest order one, where the system turns out to be more stable than the theoretical expectation. Keywords: rigid body, Nekhoroshev theory, chaotic dynamics Citation: Benettin G., Fasso F., Guzzo M.,  Long term stability of proper rotations and local chaotic motions in the perturbed Euler rigid body , Regular and Chaotic Dynamics, 2006, vol. 11, no. 1, pp. 1-17 DOI: 10.1070/RD2006v011n01ABEH000331
 Benettin G., Fasso F., Guzzo M. Nekhoroshev-stability of $L_4$ and $L_5$ in the spatial restricted three-body problem 1998, vol. 3, no. 3, pp.  56-72 Abstract We show that $L_4$ and $L_5$ in the spatial restricted circular three-body problem are Nekhoroshev-stable for all but a few values of the reduced mass up to the Routh critical value. This result is based on two extensions of previous results on Nekhoroshev-stability of elliptic equilibria, namely to the case of "directional quasi-convexity", a notion introduced here, and to a (non-convex) steep case. We verify that the hypotheses are satisfied for $L_4$ and $L_5$ by means of numerically constructed Birkhoff normal forms. Citation: Benettin G., Fasso F., Guzzo M.,  Nekhoroshev-stability of $L_4$ and $L_5$ in the spatial restricted three-body problem, Regular and Chaotic Dynamics, 1998, vol. 3, no. 3, pp. 56-72 DOI:10.1070/RD1998v003n03ABEH000080