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On the topological Kolmogorov property of the Chacon and Petersen subshifts


Authors: Wojciech Bułatek and Brunon Kamiński
Journal: Proc. Amer. Math. Soc. 139 (2011), 1735-1741
MSC (2010): Primary 37B05, 54H20; Secondary 28D05
DOI: https://doi.org/10.1090/S0002-9939-2010-10599-3
Published electronically: October 18, 2010
MathSciNet review: 2763761
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Abstract: Basic properties of a $ K$-relation, the topological analogue of the classical Kolmogorov definition, are investigated. It is shown that the Petersen subshift is a topological $ K$-system and that the Chacon subshift is not.


References [Enhancements On Off] (What's this?)

  • 1. F. Blanchard, Fully positive topological entropy and topological mixing, Contemporary Mathematics, 135, Amer. Math. Soc., 1992, pp. 95-105. MR 1185082 (93k:58134)
  • 2. F. Blanchard, Y. Lacroix, Zero entropy factors of topological flows, Proc. Amer. Math. Soc. 119 (1993) no. 3, 985-992. MR 1155593 (93m:54066)
  • 3. B. Kamiński, A. Siemaszko, J. Szymański, The determinism and the Kolmogorov property in topological dynamics, Bull. Pol. Acad. Sci. Math. 51 (2003), no. 4, 401-417. MR 2025310 (2004i:37014)
  • 4. B. Kamiński, A. Siemaszko, J. Szymański, Extreme relations for topological flows, Bull. Pol. Acad. Sci. Math. 53 (2005), no. 1, 17-24. MR 2162751 (2006c:37007)
  • 5. K. Petersen, A topologically strongly mixing symbolic minimal set, Trans. Amer. Math. Soc. 148 (1970), 603-612. MR 0259884 (41:4513)
  • 6. K. Petersen, Ergodic Theory, Cambridge University Press, Cambridge-London-New York, 1983. MR 0833286 (87i:28002)
  • 7. J. de Vries, Elements of Topological Dynamics, Kluwer Academic Publishers, Dordrecht-Boston-London, 1993. MR 1249063 (94m:54098)

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Additional Information

Wojciech Bułatek
Affiliation: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland
Email: bulatek@mat.uni.torun.pl

Brunon Kamiński
Affiliation: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland
Email: bkam@mat.uni.torun.pl

DOI: https://doi.org/10.1090/S0002-9939-2010-10599-3
Received by editor(s): March 15, 2010
Received by editor(s) in revised form: May 2, 2010, May 19, 2010, and May 21, 2010
Published electronically: October 18, 2010
Additional Notes: The first author was supported in part by Grant MNiSZW NN201 384834.
The second author was supported in part by Grant MNiSZW NN201 384834.
Communicated by: Bryna Kra
Article copyright: © Copyright 2010 American Mathematical Society

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