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On the predictability of discrete dynamical systems II

Author(s): Nilson C. Bernardes Jr.
Journal: Proc. Amer. Math. Soc. 133 (2005), 3473-3483.
MSC (2000): Primary 37B25, 37B20, 54H20; Secondary 54E52, 54C35
Posted: June 7, 2005
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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: 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
Posted: June 7, 2005
Communicated by: Alan Dow
Copyright of article: Copyright 2005, American Mathematical Society

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