Bulletin of the Belgian Mathematical Society - Simon Stevin

A note on the uniform limit of transitive dynamical systems

Alessandro Fedeli and Attilio Le Donne

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Abstract

In this note we study the dynamical behaviour of the uniform limit of a sequence of continuous self-maps on a compact metric space satisfying (topological) transitivity or other related properties. Moreover, some conditions for the transitivity of a limit are given.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 16, Number 1 (2009), 59-66.

Dates
First available in Project Euclid: 25 February 2009

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1235574192

Digital Object Identifier
doi:10.36045/bbms/1235574192

Mathematical Reviews number (MathSciNet)
MR2498959

Zentralblatt MATH identifier
1160.37314

Subjects
Primary: 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.) 40A30: Convergence and divergence of series and sequences of functions 54H20: Topological dynamics [See also 28Dxx, 37Bxx]

Keywords
(topological) transitivity chaos uniform convergence chain-transitivity shadowing property

Citation

Fedeli, Alessandro; Le Donne, Attilio. A note on the uniform limit of transitive dynamical systems. Bull. Belg. Math. Soc. Simon Stevin 16 (2009), no. 1, 59--66. doi:10.36045/bbms/1235574192. https://projecteuclid.org/euclid.bbms/1235574192


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