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

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Regular and Chaotic Dynamics, 1998, Volume 3, Issue 3, Pages 56–72
DOI: https://doi.org/10.1070/RD1998v003n03ABEH000080 (Mi rcd948)

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. Benettin^a, F. Fassò^b, M. Guzzo^b

^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

Citations (39)

DOI: https://doi.org/10.1070/RD1998v003n03ABEH000080

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

Bibliographic databases:

Document Type: Article

MSC: 58F10, 58F36, 70F07

Language: English

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

Citation in format AMSBIB

\Bibitem{BenFasGuz98}

\by G.~Benettin, F.~Fass\`o, M.~Guzzo

\paper Nekhoroshev-stability of $L_4$ and $L_5$ in the spatial restricted three-body problem

\jour Regul. Chaotic Dyn.

\yr 1998

\vol 3

\issue 3

\pages 56--72

\mathnet{http://mi.mathnet.ru/rcd948}

\crossref{https://doi.org/10.1070/RD1998v003n03ABEH000080}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1704969}

\zmath{https://zbmath.org/?q=an:0934.70010}

Linking options:

https://www.mathnet.ru/eng/rcd948

https://www.mathnet.ru/eng/rcd/v3/i3/p56

This publication is cited in the following 39 articles:

Alessandra Celletti, Encyclopedia of Complexity and Systems Science, 2023, 1
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Alessandra Celletti, Encyclopedia of Complexity and Systems Science Series, Perturbation Theory, 2022, 339
Rocío I. Paez, Massimiliano Guzzo, “On the semi-analytical construction of halo orbits and halo tubes in the elliptic restricted three-body problem”, Physica D: Nonlinear Phenomena, 439 (2022), 133402
Àngel Jorba, Encyclopedia of Complexity and Systems Science Series, Perturbation Theory, 2022, 153
Àngel Jorba, Encyclopedia of Complexity and Systems Science, 2022, 1
Carcamo-Diaz D., Palacian J.F., Vidal C., Yanguas P., “Nonlinear Stability of Elliptic Equilibria in Hamiltonian Systems With Exponential Time Estimates”, Discret. Contin. Dyn. Syst., 41:11 (2021), 5183–5208
Carcamo-Diaz D. Palacian J.F. Vidal C. Yanguas P., “Nonlinear Stability in the Spatial Attitude Motion of a Satellite in a Circular Orbit”, SIAM J. Appl. Dyn. Syst., 20:3 (2021), 1421–1463
Galgani L., “Foundations of Physics in Milan, Padua and Paris. Newtonian Trajectories From Celestial Mechanics to Atomic Physics”, Math. Eng., 3:6, SI (2021)
Daniela Cárcamo-Díaz, Jesús F. Palacián, Claudio Vidal, Patricia Yanguas, “On the Nonlinear Stability of the Triangular Points in the Circular Spatial Restricted Three-body Problem”, Regul. Chaotic Dyn., 25:2 (2020), 131–148
Bounemoura A., Fayad B., Niederman L., “Nekhoroshev Estimates For Steep Real-Analytic Elliptic Equilibrium Points”, Nonlinearity, 33:1 (2020), 1–33
Chierchia L., Faraggiana M.A., Guzzo M., “On Steepness of 3-Jet Non-Degenerate Functions”, Ann. Mat. Pura Appl., 198:6 (2019), 2151–2165
Tong Luo, Ming Xu, “Dynamics of the spatial restricted three-body problem stabilized by Hamiltonian structure-preserving control”, Nonlinear Dyn, 94:3 (2018), 1889
Ram Kishor, Badam Singh Kushvah, “Normalization of Hamiltonian and nonlinear stability of the triangular equilibrium points in non-resonance case with perturbations”, Astrophys Space Sci, 362:9 (2017)
Massimiliano Guzzo, Elena Lega, “The Nekhoroshev Theorem and the Observation of Long-term Diffusion in Hamiltonian Systems”, Regul. Chaotic Dyn., 21:6 (2016), 707–719
M. Guzzo, L. Chierchia, G. Benettin, “The Steep Nekhoroshev's Theorem”, Commun. Math. Phys., 342:2 (2016), 569
Gabriella Schirinzi, Massimiliano Guzzo, “Numerical Verification of the Steepness of Three and Four Degrees of Freedom Hamiltonian Systems”, Regul. Chaotic Dyn., 20:1 (2015), 1–18
Francesco Fassò, Debra Lewis, “Erratum Erratum to: Stability Properties of the Riemann Ellipsoids”, Arch Rational Mech Anal, 212:3 (2014), 1065
Gabriella Schirinzi, Massimiliano Guzzo, “On the formulation of new explicit conditions for steepness from a former result of N.N. Nekhoroshev”, Journal of Mathematical Physics, 54:7 (2013)
Christos Efthymiopoulos, “High order normal form stability estimates for co-orbital motion”, Celest Mech Dyn Astr, 117:1 (2013), 101

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