@incollection{SB_1998-1999__41__113_0, author = {Marmi, Stefano}, title = {Chaotic behaviour in the solar system}, booktitle = {S\'eminaire Bourbaki : volume 1998/99, expos\'es 850-864}, series = {Ast\'erisque}, note = {talk:854}, pages = {113--136}, publisher = {Soci\'et\'e math\'ematique de France}, number = {266}, year = {2000}, mrnumber = {1772672}, zbl = {0976.70009}, language = {en}, url = {http://www.numdam.org/item/SB_1998-1999__41__113_0/} }
TY - CHAP AU - Marmi, Stefano TI - Chaotic behaviour in the solar system BT - Séminaire Bourbaki : volume 1998/99, exposés 850-864 AU - Collectif T3 - Astérisque N1 - talk:854 PY - 2000 SP - 113 EP - 136 IS - 266 PB - Société mathématique de France UR - http://www.numdam.org/item/SB_1998-1999__41__113_0/ LA - en ID - SB_1998-1999__41__113_0 ER -
%0 Book Section %A Marmi, Stefano %T Chaotic behaviour in the solar system %B Séminaire Bourbaki : volume 1998/99, exposés 850-864 %A Collectif %S Astérisque %Z talk:854 %D 2000 %P 113-136 %N 266 %I Société mathématique de France %U http://www.numdam.org/item/SB_1998-1999__41__113_0/ %G en %F SB_1998-1999__41__113_0
Marmi, Stefano. Chaotic behaviour in the solar system, dans Séminaire Bourbaki : volume 1998/99, exposés 850-864, Astérisque, no. 266 (2000), Exposé no. 854, 24 p. http://www.numdam.org/item/SB_1998-1999__41__113_0/
[Ar1] Small denominators and problems of stability of motion in classical celestial mechanics, Russ. Math. Surv. 18 (1963), 85-193. | MR | Zbl
-[Ar2] Instability of dynamical systems with several degrees of freedom, Sov. Math. Dokl. 5 (1964), 581-585. | Zbl
-[Ar3] Huygens and Barrow, Newton and Hooke, Birkhäuser (1990). | MR | Zbl
-[Ar4] Dynamical Systems III, Springer-Verlag (1988). | MR | Zbl
-[B] Dynamical Systems, Amer. Math. Soc. Colloquium Pub. Vol. IX (1966).
-[Bo] Tores invariants des systèmes dynamiques hamiltoniens, Séminaire Bourbaki 639, Astérisque 133-134 (1986), 113-157. | Numdam | MR | Zbl
-[Br] Théorie du mouvement de l'ensemble des planètes. Solution VSOP82, Astron. Astrophys. 114 (1982), 278-288 | Zbl
-[Ch1] Intégration du problème de Kepler par la méthode de Hamilton-Jacobi : coordonnées "action-angles" de Delaunay, Note S026, Bureau des Longitudes, Paris (1989).
-[Ch2] À l'infini en temps fini, Séminaire Bourbaki 832, Astérisque 245 (1997), 323-353. | Numdam | MR | Zbl
-[Ce] Analysis of resonances in the spin-orbit problem in celestial mechanics: higher order resonances and some numerical experiments (Part II) ZAMP 41 (1990), 453-479. | MR | Zbl
-[CFS] Ergodic Theory, Grundlehren der mathematischen Wissenschaften 245, Springer-Verlag, Berlin-Heidelberg- New York (1982). | MR | Zbl
, , -[CMN] Long-term numerical integration and synthetic theories for the motion of outer planets, Astron. Astrophys. 181 (1987), 182-194. | Zbl
, , -[Da] Fundamentals of Celestial Mechanics, Willmann-Bell (1988). | MR
-[Gi] On the problem of stability for near to integrable Hamiltonian systems, ICM1998. | EuDML | Zbl
-[GDFGS] Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three-body problem, J. Diff. Eq. 77 (1989), 167-198. | MR | Zbl
, , , , -[GS] On the stability of the Trojan asteroids, Astron. Astrophys. 317 (1997), 254-261.
, -[Ha] Sur l'invariabilité des grands axes des orbites planétaires, Ann. Obs. Paris XVIII (1885), 11-139.
-[He1] Sur les courbes invariantes par les difféomorphismes de l'anneau, Astérisque 103-104 (1983). | Numdam | Zbl
-[He2] Some open problems in dynamical systems, ICM1998. | EuDML | Zbl
-[He3] Stability in measure in the n-body problem, seminar given at the ICTP Workshop on Dynamical Systems, Trieste (1998).
-[K] The General Theory of Dynamical Systems and Classical Mechanics, address to the 1954 International Congress of Mathematicians, Amsterdam.
-[Lg] Sur l'altération des moyens mouvements des planètes, Mem. Acad. Sci. Berlin 199 (1776) et Oeuvres Complètes VI Paris, Gauthier-Villars (1869), 255.
-[Lp1] Mémoire sur les solutions particulières des équations différentielles et sur les inégalités séculaires des planètes, (1772), Oeuvres complètes IX Paris, Gauthier-Villars (1895), 325.
-[Lp2] Mémoire sur les inégalités séculaires des planètes et des satellites, Mem. Acad. royale des Sciences de Paris (1784) and Oeuvres complètes XI Paris, Gauthier-Villars (1895), 49.
-[L1989a] Les variables de Poincaré et le développement de la fonction perturbatrice, Note S026, Bureau des Longitudes, Paris (1989).
-[L1989b] A numerical experiment on the chaotic behaviour of the Solar System, Nature 338 (1989), 237-238.
-[L1990] The chaotic behaviour of the Solar System: a numerical estimate of the size of the chaotic zones, Icarus 88 (1990), 266-291.
-[L1992] A few points on the stability of the Solar System, in "Chaos, Resonance and collective dynamical phenomena in the Solar System" Symposium IAU 152, S. Ferraz-Mello ed., Kluwer, Dordrechet (1992), 1-16.
-[L1993] Frequency analysis for multi-dimensional systems. Global dynamics and diffusion, Physica D 67 (1993), 257-281. | MR | Zbl
-[L1994] Large-scale chaos in the solar system, Astron. Astrophys. 287 (1994), L9-L12.
-[L1995a] Large scale chaos and marginal stability of the Solar System, in XI International Congress of Mathematical Physics, D. Iagolnitzer ed., International Press (1995), 75-120. | MR | Zbl
-[L1995b] Introduction to frequency map analysis, Proceedings NATO Advanced Study Institute Hamiltonian systems with three or more degrees of freedom S'Agaro, Spain, June 1995. | Zbl
-[L1996] Chaos à grande échelle dans le Système Solaire et implications planétologiques, C.R. Acad. Sci. Paris, 322 série IIa (1996), 163-180.
-[L1997] Large scale chaos and the spacing of inner planets, Astron. Astrophys. 317 (1997), L75-L78.
-[LFC] The measure of chaos by the numerical analysis of the fundamental frequencies. Application of the standard mapping, Physica D56 (1992), 253-269. | MR | Zbl
, , -[LJB] Orbital, precessional and insolation quantities for the Earth from -20Myr to +10 Myr, Astron. Astrophys. 270 (1993), 522-533.
, , -[LJR] Stabilization of the Earth's obliquity by the Moon, Nature 361 (1993), 615-617.
, , -[LRo] Application of the frequency map analysis to the ALS, Particle Accelerators 54 (1996), 183-192.
, -[LQT] Confirmation of Resonant Structure in the Solar System, Icarus 95 (1992), 148-152.
, , -[LR] The chaotic obliquity of the planets, Nature 361 (1993), 608-612.
, -[Li1] On the equilateral configuration in the restricted problem of three bodies, Proc. London Math. Soc. 9 (1959), 343-372. | MR | Zbl
-[Li2] The Lagrange configuration in Celestial Mechanics, Proc. London Math. Soc. 9 (1959), 525-543. | MR | Zbl
-[Lo] Canonical perturbation theory via simultaneous approximations, Russ. Math. Surv. 47 (1992), 57-133. | MR | Zbl
-[M] Variational construction of connecting orbits, Ann. Inst. Fourier 43 (1993), 1349-1386. | EuDML | Numdam | MR | Zbl
-[MG] Superexponential Stability of KAM Tori, J. Stat. Phys. 78 (1995), 1607-1617. | MR | Zbl
, -[MN] Numerous weak resonances drive asteroids towards terrestrial planet orbits, preprint (1998). | MR
, -[Mo] Review of the dynamics in the Kirkwood gaps, Cel. Mech. 65 (1997), 175-204. | MR | Zbl
-[N] Principia. Vol II. The System of the World, Translation Motte, Univ. of California Press.
-[Ne] An exponential estimate for the time of stability of nearly integrable Hamiltonian systems, Russ. Math. Surveys 32 (1977), 1-65. | MR | Zbl
-[Ni] Stability over exponentially long times in the planetary system, Nonlinearity 9 (1996), 1703-1751. | MR | Zbl
-[P] Les Méthodes Nouvelles de la Mécanique Céleste, tomes I-III, Paris Gauthier-Villars (1892, 1893, 1899). | JFM
-[P2] Leçons de Mécanique Céleste, tome I, Paris Gauthier-Villars (1905).
-[Po] Sur les inégalités séculaires des moyens mouvements des planètes, Journal de L'Ecole Polytechnique VIII (1809), 1.
-[Pol] Celestial Mechanics, The Carus Mathematical Monographs 18 (1976). | MR | Zbl
-[Pö] Integrability of Hamiltonian systems on Cantor sets, Comm. Pure Appl. Math. 35 (1982), 653-696. | MR | Zbl
-[Ro] Stability of the planetary three-body problem (part II), Celest. Mech. 62 (1995), 219-261. | MR | Zbl
-[SM] Lectures on Celestial Mechanics, Springer-Verlag, Berlin-Heidelberg-New York (1971). | MR | Zbl
, -[St] Celestial Mechanics I, W.A. Benjamin, New York (1969). | Zbl
-[SW] Numerical evidence that the motion of Pluto is chaotic, Science 241 (1988), 433-437.
, -[Wi] The Analytical foundations of celestial mechanics, Princeton University Press (1941). | JFM | MR
-[WPM] The chaotic rotation of Hyperion, Icarus 58 (1984), 137-152.
, , -[Y1] An introduction to small divisors problems, in "From Number Theory to Physics", M. Waldschmidt, P. Moussa, J.-M. Luck and C. Itzykson eds. Springer Verlag (1992), 659-679. | MR | Zbl
-[Y2] Introduction to Hyperbolic Dynamics, in "Real and Complex Dynamical Systems" B. Branner and P. Hjorth eds., NATO ASI Series C464, Kluwer, Dordrecht (1995), 265-291. | MR | Zbl
-[Yo] Ergodic Theory of Differentiable Dynamical Systems, in "Real and Complex Dynamical Systems" B. Branner and P. Hjorth eds., NATO ASI Series C464, Kluwer, Dordrecht (1995), 293-336. | MR | Zbl
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