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A dynamical system on $ {\bf R}\sp 3$ with uniformly bounded trajectories and no compact trajectories


Authors: K. M. Kuperberg and Coke S. Reed
Journal: Proc. Amer. Math. Soc. 106 (1989), 1095-1097
MSC: Primary 58F25; Secondary 54H20, 58F10
DOI: https://doi.org/10.1090/S0002-9939-1989-0965244-4
MathSciNet review: 965244
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Abstract: This paper contains an example of a rest point free dynamical system on $ {R^3}$ with uniformly bounded trajectories, and with no circular trajectories. The construction is based on an example of a dynamical system described by P. A. Schweitzer, and on an example of a dynamical system on $ {R^3}$ constructed previously by the authors.


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

  • [1] F. B. Fuller, An index of fixed point type for periodic orbits, Amer. J. Math. 89 (1967), 133-148. MR 0209600 (35:497)
  • [2] K. Kuperberg and C. Reed, A rest point free dynamical system on $ {R^3}$ with uniformly bounded trajectories, Fund. Math. 114 (1981), 229-234. MR 644408 (83d:54068)
  • [3] R. D. Mauldin (ed.), The Scottish book: Mathematics from the Scottish Café, Birkhauser, Boston, 1981. MR 666400 (84m:00015)
  • [4] P. A. Schweitzer, Counterexamples to the Seifert conjecture and opening closed leaves of foliations, Ann. of Math. (2) 100 (1974), 386-400. MR 0356086 (50:8557)
  • [5] S. M. Ulam, The Scottish book, Los Alamos Scientific Monograph LA-6832.
  • [6] F. W. Wilson, Jr., On the minimal sets of non-singular vector fields, Ann. of Math. (2) 84 (1966), 529-536. MR 0202155 (34:2028)

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DOI: https://doi.org/10.1090/S0002-9939-1989-0965244-4
Article copyright: © Copyright 1989 American Mathematical Society

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