Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Attractors with positively Lyapunov stable trajectories


Author: Tadeusz Nadzieja
Journal: Proc. Amer. Math. Soc. 86 (1982), 87-90
MSC: Primary 58F12; Secondary 34D20, 54H20, 70K15
DOI: https://doi.org/10.1090/S0002-9939-1982-0663873-2
MathSciNet review: 663873
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that a finite dimensional attractor in locally connected metric space consisting of positively Lyapunov stable trajectories is a torus.


References [Enhancements On Off] (What's this?)

  • [1] G. Allaud and E. S. Thomas, Almost periodic minimal sets, J. Differential Equations 15 (1974), 158-171. MR 0339289 (49:4049)
  • [2] N. P. Bhatia and G. P. Szegö, Stability theory of dynamical systems, Springer-Verlag, Berlin, 1970. MR 0289890 (44:7077)
  • [3] L. G. Deysach and G. R. Sell, On the existence of almost periodic motions, Michigan Math. J. 12 (1965), 87-95. MR 0173064 (30:3279)
  • [4] R. Engelking, Topologia ogólna, PWN, Warsaw, 1975.
  • [5] J. L. Kaplan and J. A. Yorke, The onset of chaos in a fluid flow model of Lorenz, Ann. New York Acad. Sci. 316 (1978), 400-407. MR 556845 (81a:76029)
  • [6] L. D. Landau and E. M. Lifschitz, Fluid mechanics, Pergamon Press, Oxford, 1959.
  • [7] V. V. Nemytskii and V. V. Stepanov, Qualitative theory of differential equations, Princeton Univ. Press, Princeton, N.J., 1960. MR 0121520 (22:12258)
  • [8] L. S. Pontryagin, Topological groups, 2nd ed., Gordon and Breach, New York, 1966. MR 0201557 (34:1439)
  • [9] D. Ruelle, Sensitive dependence on initial conditions and turbulent behavior of dynamical systems, Ann. New York Acad. Sci 316 (1978), 408-416. MR 556846 (82b:58048)
  • [10] -, Strange attractors, Math. Intell. 2 (1980), 126-137. MR 595080 (82b:58056)
  • [11] D. Ruelle and F. Takens, On the nature of turbulence, Comment. Math. Phys. 20 (1971), 167-192. MR 0284067 (44:1297)
  • [12] G. R. Sell, Periodic solutions and asymptotic stability, J. Differential Equations 2 (1966), 143-157. MR 0190479 (32:7891)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58F12, 34D20, 54H20, 70K15

Retrieve articles in all journals with MSC: 58F12, 34D20, 54H20, 70K15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0663873-2
Keywords: Attractor, turbulence, positively Lyapunov stable trajectory, almost periodic orbit
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society