On the set of points with a dense orbit
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- by Nilson C. Bernardes Jr. PDF
- Proc. Amer. Math. Soc. 128 (2000), 3421-3423 Request permission
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
- 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.
- 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, DOI 10.1007/BF02765019
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
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 3421-3423
- MSC (2000): Primary 37B20, 54H20
- DOI: https://doi.org/10.1090/S0002-9939-00-05438-1
- MathSciNet review: 1690975