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This article is cited in 39 scientific papers (total in 39 papers)
On the 70th birthday of J.Moser
Nekhoroshev-stability of $L_4$ and $L_5$ in the spatial restricted three-body problem
G. Benettina, F. Fassòb, M. Guzzob a Materia and Gruppo Naziotiale di Fisica Matematica (CNR),
Istituto Nazionale di Fisica della,
Dipartimento di Matematica Pura e Applicata,
Via G. Belzoni 7, 35131 Padova, Italy
b Gruppo Naziotiale di Fisica Matematica (CNR.),
Dipartimento di Matematica Pura e Applicata,
Via G. Belzoni 7, 35131 Padova, Italy
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.
Received: 07.10.1998
Citation:
G. Benettin, F. Fassò, M. Guzzo, “Nekhoroshev-stability of $L_4$ and $L_5$ in the spatial restricted three-body problem”, Regul. Chaotic Dyn., 3:3 (1998), 56–72
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https://www.mathnet.ru/eng/rcd948 https://www.mathnet.ru/eng/rcd/v3/i3/p56
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