Préprints et publications

• 2024
• Note on the attraction of an ellipsoid in a spherical universe
  Alain Albouy
  Accepté dans Proceedings of the Steklov Institute of Mathematics
  http://arxiv.org/abs/2408.12453
• Bounded orbits for three bodies in ℝ⁴
  Alain Albouy, Holger R. Dullin
  Paru dans Geometric Mechanics, 1 (2024), 2450003
  https://www.worldscientific.com/doi/10.1142/S2972458924500035
  http://arxiv.org/abs/2309.14579
• A limit of nonplanar 5-body central configurations is nonplanar
  Alain Albouy, Antonio Carlos Fernandes
  Paru dans Archive for Rational Mechanics and Analysis, 248 (2024), 12
  https://rdcu.be/dxukm
  http://arxiv.org/abs/2308.12901

• 2023
• How many Keplerian arcs are there between two points of spacetime?
  Alain Albouy, Antonio J. Ureña
  Paru dans Celestial Mechanics and Dynamical Astronomy, 135 (2023), 18
  https://rdcu.be/c9pWg
  http://arxiv.org/abs/2302.06013
• An antimaximum principle for periodic solutions of a forced oscillator
  Alain Albouy, Antonio J. Ureña
  Paru dans Communications in Contemporary Mathematics, 25 (2023), 2250041
  https://www.worldscientific.com/doi/10.1142/S0219199722500419
  http://arxiv.org/abs/2201.09272

• 2022
• Darboux inversions of the Kepler problem
  Alain Albouy, Lei Zhao
  Paru dans Regular and Chaotic Dynamics, 27 (2022), 253-280
  https://rdcu.be/cORTU
  http://arxiv.org/abs/2201.00808

• 2020
• Relative Equilibria of the 3-body Problem in ℝ⁴
  Alain Albouy, Holger R. Dullin
  Paru dans Journal of Geometric Mechanics, 12 (2020), 323-341
  http://www.aimsciences.org/article/doi/10.3934/jgm.2020012
  https://arxiv.org/abs/2002.00649
• Some simple results about the Lambert problem
  Alain Albouy, Antonio J. Ureña
  Paru dans The European Physical Journal Special Topics, 229 (2020), 1405-1417
  https://rdcu.be/b4vJB
  https://arxiv.org/abs/2001.09301

• 2019
• Lambert's theorem and projective dynamics
  Alain Albouy, Lei Zhao
  Paru dans Philosophical Transactions of the Royal Society A: mathematical, physical and engineering sciences, 377 (2019)
  https://royalsocietypublishing.org/doi/10.1098/rsta.2018.0417
  http://arxiv.org/abs/1910.05391
• Lambert's Theorem: Geometry or Dynamics?
  Alain Albouy
  Paru dans Celestial Mechanics and Dynamical Astronomy, 131 (2019), 40
  https://rdcu.be/bPCLg
  https://arxiv.org/abs/1711.03049

• 2015
• Are Palmore's «ignored estimates» on the number of planar central configurations correct?
  Alain Albouy
  Paru dans Qualitative Theory of Dynamical Systems, 14 (2015), 403-406
  http://arxiv.org/abs/1501.00694
• Projective dynamics and first integrals
  Alain Albouy
  Paru dans Regular and Chaotic Dynamics, 20 (2015), 247-276
  http://link.springer.com/article/10.1134/S1560354715030041
  (version préliminaire : http://arxiv.org/abs/math-ph/0612031)
  (pdf, 0.6 Mo)

• 2014
• Some remarks about Descartes' rule of signs
  Alain Albouy, Yanning Fu
  Paru dans Elemente der Mathematik, 69 (2014), 186-194
  http://www.ems-ph.org/journals/show_abstract.php?issn=0013-6018&vol=69&iss=4&rank=3
  http://arxiv.org/abs/1307.6842
• On the force fields which are homogeneous of degree -3
  Alain Albouy
  Paru dans Extended Abstracts Spring 2014, Volume 4 of the series Trends in Mathematics pp. 3-7
  http://arxiv.org/abs/1412.4150

• 2013
• There is a projective dynamics
  Alain Albouy
  Paru dans EMS Newsletter, 89 (September 2013), 37-43
  http://www.ems-ph.org/journals/all_issues.php?issn=1027-488X
• Histoire des équations de la mécanique analytique: repères chronologiques et difficultés
  Alain Albouy
  Paru dans Siméon-Denis Poisson. Les mathématiques au service de la science, Yvette Kosmann-Schwarzbach, éd., Éditions de l'École Polytechnique, Palaiseau (2013), 229-279
  http://www.editions.polytechnique.fr/?afficherfiche=187

• 2012
• Some problems on the classical n-body problem
  Alain Albouy, Hildeberto E. Cabral, Alan A. Santos
  Paru dans Celestial Mechanics and Dynamical Astronomy, 113 (2012), 369-375
  http://link.springer.com/article/10.1007%2Fs10569-012-9431-1
  http://arxiv.org/abs/1305.3191
• Finiteness of central configurations of five bodies in the plane
  Alain Albouy, Vadim Kaloshin
  Paru dans Annals of Mathematics 176 (2012), 535-588
  http://annals.math.princeton.edu/2012/176-1/p10

• 2009
• Relative equilibria of four identical satellites
  Alain Albouy, Yanning Fu
  Paru dans Proc. R. Soc. A, 465 (2009), 2633-2645
  http://rspa.royalsocietypublishing.org/content/465/2109/2633.abstract
  (version préliminaire : http://arxiv.org/abs/0902.3215v1)

• 2008
• Symmetry of Planar Four-Body Convex Central Configurations
  Alain Albouy, Yanning Fu, Shanzhong Sun
  Paru dans Proc. R. Soc. A, 464 (2008), 1355-1365
  http://rspa.royalsocietypublishing.org/content/464/2093/1355.abstract
  (version préliminaire : http://arxiv.org/abs/0706.1194)
• Projective dynamics and classical gravitation
  Alain Albouy
  Paru dans Regular and Chaotic Dynamics, 13 (2008), 525-542
  http://link.springer.com/article/10.1134%2FS156035470806004X
  (version préliminaire : http://arxiv.org/abs/math-ph/0501026)

• 2007
• Euler configurations and quasi-polynomial systems
  Alain Albouy, Yanning Fu
  Paru dans Regular and Chaotic Dynamics, 12 (2007), 39-55
  http://link.springer.com/article/10.1134%2FS1560354707010042
  (version préliminaire : http://arxiv.org/abs/math-ph/0603075)
• Projective dynamics of a classical particle or multiparticle system
  Alain Albouy
  Oberwolfach reports, No 33/2007, 1926-1928
  http://www.ems-ph.org/journals/show_abstract.php?issn=1660-8933&vol=4&iss=3&rank=5
  (pdf, 117 Ko)
• Some classical integrable problems
  Alain Albouy
  Lecture in Hanoi
  (pdf, 920 Ko)

• 2004
• Mutual Distances in Celestial Mechanics
  Alain Albouy
  Lectures at Nankai Institute, Tianjin, Chine, juin 2004
  (pdf, 200 Ko)
• Generalizing the classical fixed-centres problem in a non-Hamiltonian way
  Alain Albouy, Teresinha Stuchi
  Paru dans J. Phys. A, Math. Gen. 37 (2004), 9109-9123
  http://iopscience.iop.org/0305-4470/37/39/005

• 2003
• The underlying geometry of the fixed centers problems
  Alain Albouy
  Paru dans Topological Methods, Variational Methods and their applications,
  edited by H. Brezis, K.C. Chang, S.J. Li and P. Rabinowitz, World Scientific (2003), 11-21
  http://books.google.com/books?id=7OBw6HDji88C&pg=PA11
• Histoire des équations de Newton. Un demi-siècle d'incompréhension
  Alain Albouy
  Journées Scientifiques de l'Institut de Mécanique Céleste
  (pdf, 111 Ko)
• Generalized Euler's Configurations and Kushnirenko Problem
  Alain Albouy
  (pdf, 121 Ko)
• On a paper of Moeckel on Central Configurations
  Alain Albouy
  Paru dans Regular and Chaotic Dynamics, 8 (2003), 133-142
  http://www.turpion.org/php/paper.phtml?journal_id=rd&paper_id=232&year_id=2003&volume=8&issue_id=2&fpage=133&lpage=142
  (pdf, 139 Ko)

• 2002
• Spatial central configurations for the 1+4 body problem
  Alain Albouy, Jaume Llibre
  Paru dans Contemporary Mathematics, 292 (2002), 1-16
  https://books.google.fr/books?id=MG8bCAAAQBAJ

• 2001
• On a strange resonance noticed by M. Herman
  Khaled Abdullah, Alain Albouy
  Paru dans Regular and Chaotic Dynamics, 6 (2001), 421-432
  http://www.turpion.org/php/paper.phtml?journal_id=rd&paper_id=186&year_id=2001&volume=6&issue_id=4&fpage=421&lpage=432
  (pdf, 151 Ko)

• 2000
• The Inverse Problem for Collinear Central Configurations
  Alain Albouy, Richard Moeckel
  Paru dans Celestial Mechanics and Dynamical Astronomy, 77 (2000), 77-91
  http://link.springer.com/article/10.1023%2FA%3A1008345830461

• 1998
• Le problème des N corps et les distances mutuelles
  Alain Albouy, Alain Chenciner
  Paru dans Inventiones Mathematicae 131 (1998), 151-184
  http://link.springer.com/article/10.1007%2Fs002220050200

• 1997
• Recherches sur le problème des n corps
  Alain Albouy
  Notes scientifiques et techniques du Bureau des Longitudes
  ISSN 1243-4272, ISBN 2-910015-18-1
  
https://www.imcce.fr/content/medias/publications/publications-recherche/nst/docs/S058.pdf
(pdf, 2.1 Mo)

• 1996
• The symmetric central configurations of four equal masses
  Alain Albouy
  Paru dans Contemporary Mathematics 198 (1996), 131-135
  https://books.google.fr/books?id=EtEaCAAAQBAJ
  (pdf, 124 Ko)

• 1995
• Symétrie des configurations centrales de quatre corps
  Alain Albouy
  Paru dans C. R. Acad. Sci. Paris 320, série 1 (1995), 217-220
  http://gallica.bnf.fr/ark:/12148/bpt6k5812512r/f99.image
  (pdf, 678 Ko)

• 1993
• Integral manifolds of the N-body problem
  Alain Albouy
  Paru dans Inventiones Mathematicae, 114 (1993), 463-488
  https://resolver.sub.uni-goettingen.de/purl?PPN356556735_0114
  http://link.springer.com/article/10.1007%2FBF01232677
  (pdf, 263 Ko)