General information
Latest issue
Forthcoming papers
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Mat. Sb.:

Personal entry:
Save password
Forgotten password?

Mat. Sb. (N.S.), 1969, Volume 78(120), Number 1, Pages 3–50 (Mi msb3540)  

This article is cited in 46 scientific papers (total in 46 papers)

Quasirandom dynamical systems. III. Quasirandom oscillations of one-dimensional oscillators

V. M. Alekseev

Full text: PDF file (4479 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1969, 7:1, 1–43

Bibliographic databases:

UDC: 519.28+519.54
MSC: 35B05, 37H10, 37E30, 37C05, 35K10, 37C70
Received: 17.06.1968

Citation: V. M. Alekseev, “Quasirandom dynamical systems. III. Quasirandom oscillations of one-dimensional oscillators”, Mat. Sb. (N.S.), 78(120):1 (1969), 3–50; Math. USSR-Sb., 7:1 (1969), 1–43

Citation in format AMSBIB
\by V.~M.~Alekseev
\paper Quasirandom dynamical systems. III.~Quasirandom oscillations of one-dimensional oscillators
\jour Mat. Sb. (N.S.)
\yr 1969
\vol 78(120)
\issue 1
\pages 3--50
\jour Math. USSR-Sb.
\yr 1969
\vol 7
\issue 1
\pages 1--43

Linking options:

    SHARE: FaceBook Twitter Livejournal

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
    Cycle of papers

    This publication is cited in the following articles:
    1. S. Smeil, “Differentsiruemye dinamicheskie sistemy”, UMN, 25:1(151) (1970), 113–185  mathnet  mathscinet
    2. Richard McGehee, “A stable manifold theorem for degenerate fixed points with applications to celestial mechanics”, Journal of Differential Equations, 14:1 (1973), 70  crossref
    3. David L. Rod, “Pathology of invariant sets in the monkey saddle”, Journal of Differential Equations, 14:1 (1973), 129  crossref
    4. Richard C Churchill, “Invariant sets which carry cohomology”, Journal of Differential Equations, 13:3 (1973), 523  crossref
    5. E. Zehnder, “Homoclinic points near elliptic fixed points”, Comm. Pure Appl. Math, 26:2 (1973), 131  crossref
    6. M. Voitkovski, “Simvolicheskaya dinamika v odnoi bilyardnoi zadache”, UMN, 32:3(195) (1977), 153–154  mathnet  mathscinet  zmath
    7. Jaume Llibre, Carles Simó, “Some homoclinic phenomena in the three-body problem”, Journal of Differential Equations, 37:3 (1980), 444  crossref
    8. V. M. Alekseev, “Final motions in the three-body problem and symbolic dynamics”, Russian Math. Surveys, 36:4 (1981), 181–200  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. R. V. Plykin, “On the geometry of hyperbolic attractors of smooth cascades”, Russian Math. Surveys, 39:6 (1984), 85–131  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    10. Robert W Easton, “Parabolic orbits in the planar three body problem”, Journal of Differential Equations, 52:1 (1984), 116  crossref
    11. Clark Robinson, “Homoclinic orbits and oscillation for the planar three-body problem”, Journal of Differential Equations, 52:3 (1984), 356  crossref
    12. Maciej Wojtkowski, “Invariant families of cones and Lyapunov exponents”, Ergod Th Dynam Sys, 5:1 (1985)  crossref  mathscinet  zmath
    13. Jaume Llibre, Regina Martínez, Carles Simó, “Tranversality of the invariant manifolds associated to the Lyapunov family of periodic orbits near L2 in the restricted three-body problem”, Journal of Differential Equations, 58:1 (1985), 104  crossref
    14. L. D. Pustyl'nikov, “On oscillatory motions in a certain dynamical system”, Math. USSR-Izv., 31:2 (1988), 325–347  mathnet  crossref  mathscinet  zmath
    15. S. L. Ziglin, “Splitting of the separatrices and the nonexistence of first integrals in systems of differential equations of Hamiltonian type with two degrees of freedom”, Math. USSR-Izv., 31:2 (1988), 407–421  mathnet  crossref  mathscinet  zmath
    16. G. Troll, U. Smilansky, “A simple model for chaotic scattering”, Physica D: Nonlinear Phenomena, 35:1-2 (1989), 34  crossref
    17. A. Knauf, “On soft billiard systems”, Physica D: Nonlinear Phenomena, 36:3 (1989), 259  crossref
    18. P Eckelt, E Zienicke, J Phys A Math Gen, 24:1 (1991), 153  crossref  mathscinet  zmath  adsnasa
    19. Ya. B. Pesin, “Dynamical systems with generalized hyperbolic attractors: hyperbolic, ergodic and topological properties”, Ergod Th Dynam Sys, 12:1 (1992)  crossref  mathscinet  zmath
    20. Yu.B. Suris, “Splitting of separatrices and symbolic dynamics for some degenerate standard-like maps”, Physica D: Nonlinear Phenomena, 63:3-4 (1993), 243  crossref
    21. A G Ramm, G P Berman, J Phys A Math Gen, 27:18 (1994), 6157  crossref  mathscinet  zmath  adsnasa
    22. M. B. Tabanov, “Separatrices splitting for Birkhoff’s billiard in symmetric convex domain, closed to an ellipse”, Chaos, 4:4 (1994), 595  crossref  mathscinet  zmath  adsnasa  isi
    23. Maciejewski A., “Nonintegrability of the Planar Oscillations of a Satellite”, Acta Astron., 45:1 (1995), 327–344  isi
    24. S. A. Dovbysh, “Transversal intersection of separatrices, the structure of the set of quasi-stochastic motions and the non-existence of an analytic integral in multidimensional systems”, Russian Math. Surveys, 51:4 (1996), 730–731  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    25. K. Zare, S. Chesley, “Order and chaos in the planar isosceles three-body problem”, Chaos, 8:2 (1998), 475  crossref  mathscinet  zmath  adsnasa  isi
    26. L. D. Pustyl'nikov, “On the measure of one-way oscillating motions for the Kolmogorov model and its generalization in the $n$-body problem”, Russian Math. Surveys, 53:5 (1998), 1102–1103  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    27. Henri Waelbroeck, Federico Zertuche, J Phys A Math Gen, 32:1 (1999), 175  crossref  mathscinet  zmath
    28. S. L. Ziglin, “Integrals in Involution for Groups of Linear Symplectic Transformations and Natural Mechanical Systems with Homogeneous Potential”, Funct. Anal. Appl., 34:3 (2000), 179–187  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    29. V. G. Gelfreich, V. F. Lazutkin, “Splitting of separatrices: perturbation theory and exponential smallness”, Russian Math. Surveys, 56:3 (2001), 499–558  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    30. Juan J. Morales-Ruiz, “Meromorphic nonintegrability of Hamiltonian systems”, Reports on Mathematical Physics, 48:1-2 (2001), 183  crossref
    31. Arvind Ayyer, Mikko Stenlund, “Exponential decay of correlations for randomly chosen hyperbolic toral automorphisms”, Chaos, 17:4 (2007), 043116  crossref  mathscinet  adsnasa  isi
    32. R. Moeckel, “Symbolic dynamics in the planar three-body problem”, Reg Chaot Dyn, 12:5 (2007), 449  crossref  mathscinet  isi
    33. Jaume Llibre, Rafael Ortega, “On the Families of Periodic Orbits of the Sitnikov Problem”, SIAM J Appl Dyn Syst, 7:2 (2008), 561  crossref  mathscinet  isi
    34. Rob Sturman, Stephen Wiggins, “Eulerian indicators for predicting and optimizing mixing quality”, New J Phys, 11:7 (2009), 075031  crossref  isi
    36. Kening Lu, Qiudong Wang, “Chaos in differential equations driven by a nonautonomous force”, Nonlinearity, 23:11 (2010), 2935  crossref
    37. Vladislav V. Sidorenko, “On the circular Sitnikov problem: the alternation of stability and instability in the family of vertical motions”, Celest Mech Dyn Astr, 2011  crossref
    38. Qiudong Wang, Ali Oksasoglu, “Strange attractors and their periodic repetition”, Chaos, 21:1 (2011), 013128  crossref  elib
    39. Kening Lu, Qiudong Wang, “Chaotic behavior in differential equations driven by a Brownian motion”, Journal of Differential Equations, 2011  crossref
    40. Kalas V.O., Krasilnikov P.S., “Ob ustoichivosti ravnovesiya v zadache sitnikova”, Kosmicheskie issledovaniya, 49:6 (2011), 551–551  elib
    41. Luis Barreira, Davor Dragičević, Claudia Valls, “Lyapunov Functions and Cone Families”, J Stat Phys, 2012  crossref
    42. O. M. Kiselev, “Oscillations near a separatrix in the Duffing equation”, Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 82–94  mathnet  crossref  isi  elib
    43. L. P. Pandey, I. Ahmad, “Periodic orbits and bifurcations in the Sitnikov four-body problem when all primaries are oblate”, Astrophys Space Sci, 2013  crossref
    44. Jun Shen, Kening Lu, Weinian Zhang, “Heteroclinic chaotic behavior driven by a Brownian motion”, Journal of Differential Equations, 2013  crossref
    45. Luis Barreira, Davor Dragičević, Claudia Valls, “Positive top Lyapunov exponent via invariant cones: Single trajectories”, Journal of Mathematical Analysis and Applications, 2014  crossref
    46. S. V. Bolotin, D. V. Treschev, “The anti-integrable limit”, Russian Math. Surveys, 70:6 (2015), 975–1030  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:390
    Full text:144

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020