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)

 

 

Unstable weak attractors


Author: Ronald A. Knight
Journal: Proc. Amer. Math. Soc. 86 (1982), 586-590
MSC: Primary 58F12; Secondary 34D99, 54H20
DOI: https://doi.org/10.1090/S0002-9939-1982-0674085-0
MathSciNet review: 674085
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Our objective in this paper is to continue the process of classification and characterization of weak attractors initiated by the author in an earlier paper. In particular, we obtain additional characterizations of those weak attractors which are saddle sets and bilateral weak attractors.


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

  • [1] Nam P. Bhatia, Dynamical systems, Mathematical systems theory and economics, I, II (Proc. Internat. Summer School, Varenna, 1967) Springer, Berlin, 1969, pp. 1–9. Lecture Notes in Operations Research and Mathematical Economics, Vols. 11, 12. MR 0324143
  • [2] N. P. Bhatia and O. Hájek, Local semi-dynamical systems, Lecture Notes in Mathematics, Vol. 90, Springer-Verlag, Berlin-New York, 1969. MR 0251328
  • [3] N. P. Bhatia and G. P. Szegö, Stability theory of dynamical systems, Die Grundlehren der mathematischen Wissenschaften, Band 161, Springer-Verlag, New York-Berlin, 1970. MR 0289890
  • [4] R. Knight, Zubov's condition revisited, Proc. Edinburgh Math. Soc. (to appear).
  • [5] Dennis Sullivan, A counterexample to the periodic orbit conjecture, Inst. Hautes Études Sci. Publ. Math. 46 (1976), 5–14. MR 0501022

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58F12, 34D99, 54H20

Retrieve articles in all journals with MSC: 58F12, 34D99, 54H20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0674085-0
Keywords: Attractor, dynamical system, flow, recursive attractor, recursive weak attractor, saddle set, stable, strong attraction, weak attractor
Article copyright: © Copyright 1982 American Mathematical Society