Existence of partially hyperbolic motions in the $N$-body problem
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- by J. M. Burgos
- Proc. Amer. Math. Soc. 150 (2022), 1729-1733
- DOI: https://doi.org/10.1090/proc/15778
- Published electronically: January 5, 2022
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Abstract:
In the context of the Newtonian $N$-body problem, we prove the existence of a partially hyperbolic motion with prescribed positive energy and any initial collisionless configuration. Moreover, it is a free time minimizer of the respective supercritical Newtonian action or equivalently a geodesic ray for the respective Jacobi-Maupertuis metric.References
- A. Chenciner, Action minimizing solutions of the Newtonian $n$-body problem: from homology to symmetry, Proceedings of the International Congress of Mathematicians, Vol. III (Beijing, 2002) Higher Ed. Press, Beijing, 2002, pp. 279–294. MR 1957539
- Jean Chazy, Sur l’allure du mouvement dans le problème des trois corps quand le temps croît indéfiniment, Ann. Sci. École Norm. Sup. (3) 39 (1922), 29–130 (French). MR 1509241, DOI 10.24033/asens.739
- Davide L. Ferrario and Susanna Terracini, On the existence of collisionless equivariant minimizers for the classical $n$-body problem, Invent. Math. 155 (2004), no. 2, 305–362. MR 2031430, DOI 10.1007/s00222-003-0322-7
- C. Marchal, How the method of minimization of action avoids singularities, Celestial Mech. Dynam. Astronom. 83 (2002), no. 1-4, 325–353. Modern celestial mechanics: from theory to applications (Rome, 2001). MR 1956531, DOI 10.1023/A:1020128408706
- Christian Marchal and Donald G. Saari, On the final evolution of the $n$-body problem, J. Differential Equations 20 (1976), no. 1, 150–186. MR 416150, DOI 10.1016/0022-0396(76)90101-7
- Ezequiel Maderna and Andrea Venturelli, Viscosity solutions and hyperbolic motions: a new PDE method for the $N$-body problem, Ann. of Math. (2) 192 (2020), no. 2, 499–550. MR 4151083, DOI 10.4007/annals.2020.192.2.5
- H. Poincaré, Sur les solutions périodiques et le principe de moindre action, C. R. Acad. Sci. Paris Sér. I Math. 123 (1896), no. 1, 915–918.
Bibliographic Information
- J. M. Burgos
- Affiliation: Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados, Av. Instituto Politécnico Nacional 2508, Col. San Pedro Zacatenco, C.P. 07360 Ciudad de México, México
- MR Author ID: 1013178
- Email: burgos@math.cinvestav.mx
- Received by editor(s): April 23, 2021
- Received by editor(s) in revised form: July 16, 2021
- Published electronically: January 5, 2022
- Communicated by: Wenxian Shen
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 1729-1733
- MSC (2020): Primary 70F10, 70H20; Secondary 37J51
- DOI: https://doi.org/10.1090/proc/15778
- MathSciNet review: 4375759