When lower entropy implies stronger Devaney chaos
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- by Grzegorz Harańczyk and Dominik Kwietniak PDF
- Proc. Amer. Math. Soc. 137 (2009), 2063-2073 Request permission
Abstract:
It is proved that the infimum of the topological entropy of continuous topologically exact interval (circle) maps is strictly smaller than the infimum of the topological entropy of continuous interval (circle) maps, which are topologically mixing, but not exact. Interpreting this result in terms of popular notions of chaos, one may say that on the interval (circle) lower entropy implies stronger Devaney chaos. Moreover, the infimum of the entropy of mixing circle maps is computed. These theorems may be considered as a completion of some results of Alsedà, Kolyada, Llibre, and Snoha (1999).References
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Additional Information
- Grzegorz Harańczyk
- Affiliation: Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland
- Email: gharanczyk@gmail.com
- Dominik Kwietniak
- Affiliation: Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland
- MR Author ID: 773622
- Email: dominik.kwietniak@gmail.com
- Received by editor(s): August 18, 2008
- Published electronically: December 15, 2008
- Additional Notes: The second author was supported in part by the Ministry of Science and Education grant no. N 201 2723 33 for the years 2007–2009.
- Communicated by: Jane M. Hawkins
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 2063-2073
- MSC (2000): Primary 37B40, 37B20; Secondary 37E05, 37E10
- DOI: https://doi.org/10.1090/S0002-9939-08-09756-6
- MathSciNet review: 2480288