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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 predictability of discrete dynamical systems II


Author: Nilson C. Bernardes Jr.
Journal: Proc. Amer. Math. Soc. 133 (2005), 3473-3483
MSC (2000): Primary 37B25, 37B20, 54H20; Secondary 54E52, 54C35
Published electronically: June 7, 2005
MathSciNet review: 2163582
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Abstract: Given a metrizable compact topological $n$-manifold $X$ with boundary and a metric $d$ compatible with the topology of $X$, we prove that ``most'' continuous functions $f : X \to X$are non-sensitive at ``most'' points of $X$but are sensitive at every point of an infinite set which is dense in the set of all periodic points of $f$. We also establish some results concerning sets of periodic points and non-wandering points.


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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07924-4
PII: S 0002-9939(05)07924-4
Keywords: Topological manifolds, continuous functions, Baire category, measures, non-sensitivity, periodic points, non-wandering points
Received by editor(s): October 2, 2002
Received by editor(s) in revised form: July 2, 2004
Published electronically: June 7, 2005
Communicated by: Alan Dow
Article copyright: © Copyright 2005 American Mathematical Society