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On the set of points with a dense orbit

Author(s): Nilson C. Bernardes Jr.
Journal: Proc. Amer. Math. Soc. 128 (2000), 3421-3423.
MSC (2000): Primary 37B20, 54H20
Posted: May 18, 2000
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Abstract | References | Similar articles | Additional information

Abstract:

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

References:

[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, 2: Hypercyclic operators, Israel J. Math. 63 (1988), 1-40. MR 90b:47013


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