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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the set of points with a dense orbit


Author: Nilson C. Bernardes Jr.
Journal: Proc. Amer. Math. Soc. 128 (2000), 3421-3423
MSC (2000): Primary 37B20, 54H20
Published electronically: May 18, 2000
MathSciNet review: 1690975
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Abstract | References | Similar Articles | Additional Information

Abstract:

Under certain conditions on the topological space $X$ we prove that for every continuous map $f : X \to X$ the set of all points with a dense orbit has empty interior in $X$. This result implies a negative answer to two problems proposed by M. Barge and J. Kennedy.


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

  • [1] M. Barge and J. Kennedy, Continuum theory and topological dynamics. In Open Problems in Topology, J. van Mill and G. M. Reed, editors, pages 633-644. Elsevier Science Publishers B. V. (North-Holland), 1990. CMP 91:03
  • [2] C. J. Read, The invariant subspace problem for a class of Banach spaces. II. Hypercyclic operators, Israel J. Math. 63 (1988), no. 1, 1–40. MR 959046 (90b:47013), http://dx.doi.org/10.1007/BF02765019

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Additional Information

Nilson C. Bernardes Jr.
Affiliation: Instituto de Matemática, Universidade Federal Fluminense, Rua Mário Santos Braga s/n, Niterói, RJ, 24020-140, Brasil
Email: ganncbj@vm.uff.br

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05438-1
PII: S 0002-9939(00)05438-1
Received by editor(s): October 19, 1998
Received by editor(s) in revised form: January 22, 1999
Published electronically: May 18, 2000
Communicated by: Alan Dow
Article copyright: © Copyright 2000 American Mathematical Society