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Russian Mathematical Surveys, 1963, Volume 18, Issue 6, Pages 85–191
DOI: https://doi.org/10.1070/RM1963v018n06ABEH001143
(Mi rm6441)
 

This article is cited in 692 scientific papers (total in 694 papers)

Small denominators and problems of stability of motion in classical and celestial mechanics

V. I. Arnol'd
Received: 16.04.1963
Bibliographic databases:
Document Type: Article
Language: English
Original paper language: Russian
Citation: V. I. Arnol'd, “Small denominators and problems of stability of motion in classical and celestial mechanics”, Russian Math. Surveys, 18:6 (1963), 85–191
Citation in format AMSBIB
\Bibitem{Arn63}
\by V.~I.~Arnol'd
\paper Small denominators and problems of stability of motion in classical and celestial mechanics
\jour Russian Math. Surveys
\yr 1963
\vol 18
\issue 6
\pages 85--191
\mathnet{http://mi.mathnet.ru/eng/rm6441}
\crossref{https://doi.org/10.1070/RM1963v018n06ABEH001143}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=170705}
\zmath{https://zbmath.org/?q=an:0135.42701}
Linking options:
  • https://www.mathnet.ru/eng/rm6441
  • https://doi.org/10.1070/RM1963v018n06ABEH001143
  • https://www.mathnet.ru/eng/rm/v18/i6/p91
    Erratum
    This publication is cited in the following 694 articles:
    1. Jordi-Lluís Figueras, Alex Haro, “Sun–Jupiter–Saturn System May Exist: A Verified Computation of Quasiperiodic Solutions for the Planar Three-Body Problem”, J Nonlinear Sci, 35:1 (2025)  crossref
    2. Chiara Caracciolo, Jordi-Lluís Figueras, Alex Haro, “A parametrization algorithm to compute lower dimensional elliptic tori in Hamiltonian systems”, Nonlinearity, 38:2 (2025), 025005  crossref
    3. Bhanu Kumar, Rodney L. Anderson, Rafael de la Llave, “Rapid GPU-Assisted Search and Parameterization-Based Refinement and Continuation of Connections between Tori in Periodically Perturbed Planar Circular Restricted 3-Body Problems”, SIAM J. Appl. Dyn. Syst., 24:1 (2025), 219  crossref
    4. Anatoly Neishtadt, Alexey Okunev, “Averaging and Passage Through Resonances in Two-Frequency Systems Near Separatrices”, Commun. Math. Phys., 406:3 (2025)  crossref
    5. Guillermo Sánchez-Garrido Campos, Ángela M. Zafra, Marta Estévez-Rodríguez, Isabel Cordones, Giulio Ruffini, Javier Márquez-Ruiz, “Preclinical insights into gamma-tACS: foundations for clinical translation in neurodegenerative diseases”, Front. Neurosci., 19 (2025)  crossref
    6. Henk W. Broer, Heinz Hanßmann, Florian Wagener, “Parametrised KAM Theory, an Overview”, Regul. Chaot. Dyn., 2025  crossref
    7. Haniyeh Fallah, Andrey L. Shilnikov, “Quasi-Periodicity at Transition from Spiking to Bursting in the Pernarowski Model of Pancreatic Beta Cells”, Regul. Chaotic Dyn., 29:1 (2024), 100–119  mathnet  crossref
    8. Linda E. Reichl, “Chaos-Assisted Tunneling”, Entropy, 26:2 (2024), 144  crossref
    9. Zhaowei Lou, Youchao Wu, “KAM theorem for degenerate infinite-dimensional reversible systems”, ejde, 2024:01-?? (2024), 02  crossref
    10. B. S. Bardin, A. A. Savin, “On the Orbital Stability of Pendulum Motions of a Rigid Body in the Hess Case”, Dokl. Math., 2024  crossref
    11. Andrew Clarke, Jacques Fejoz, Marcel Guardia, “A Counterexample to the Theorem of Laplace–Lagrange on the Stability of Semimajor Axes”, Arch Rational Mech Anal, 248:2 (2024)  crossref
    12. Donato Scarcella, “Biasymptotically Quasi-Periodic Solutions for Time-Dependent Hamiltonians”, Regul. Chaotic Dyn., 29:4 (2024), 620–653  mathnet  crossref
    13. K. B. Sabitov, “The Dirichlet problem for inhomogeneous mixed-type equation with Lavrent'ev–Bitsadze operator”, Izv. Math., 88:4 (2024), 655–677  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    14. Gabriella Pinzari, “Perturbation theory and canonical coordinates in celestial mechanics”, Rev. Math. Phys., 36:05 (2024)  crossref
    15. Robert B. Mann, “One-Dimensional Relativistic Self-Gravitating Systems”, Entropy, 26:7 (2024), 612  crossref
    16. Hua Yan, Marko Robnik, “Chaos and quantization of the three-particle generic Fermi-Pasta-Ulam-Tsingou model. I. Density of states and spectral statistics”, Phys. Rev. E, 109:5 (2024)  crossref
    17. Inmaculada Baldomá, Ernest Fontich, Pau Martín, “Invariant Manifolds of Degenerate Tori and Double Parabolic Orbits to Infinity in the $(n+2)$-Body Problem”, Arch Rational Mech Anal, 248:3 (2024)  crossref
    18. B. S. Bardin, “On the Orbital Stability of Periodic Motions of a Heavy Rigid Body in the Bobylev – Steklov Case”, Rus. J. Nonlin. Dyn., 20:1 (2024), 127–140  mathnet  crossref
    19. Yury Vetyukov, Alexander Humer, Alois Steindl, “Nonlinear dynamics of a flexible rod partially sliding in a rigid sleeve under the action of gravity and configurational force”, Journal of the Mechanics and Physics of Solids, 193 (2024), 105854  crossref
    20. S. Malikis, V. Cheianov, “Integrability and chaos in the quantum brachistochrone problem”, Phys. Rev. A, 110:2 (2024)  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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