Weak mixing in general semiflows implies multi-sensitivity, but not thick sensitivity
Volume 12, Issue 2, pp 120--123
http://dx.doi.org/10.22436/jnsa.012.02.05
Publication Date: October 18, 2018
Submission Date: December 31, 2017
Revision Date: August 07, 2018
Accteptance Date: August 23, 2018
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2015
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Authors
Alica Miller
- Department of Mathematics, University of Louisville, USA.
Abstract
It was proved by Wang et al. [Wang, J. Yin, Q. Yan, J. Nonlinear Sci. Appl., \({\bf 9}\) (2016), 989--997] that any weakly mixing semiflow on a compact metric space, whose all transition maps are surjective, is thickly sensitive. We consider what happens if we do not have the assumptions of compactness and surjectivity. We prove that even in that case any weakly mixing semiflow is multi-sensitive, and that, however, it does not have to be thickly sensitive.
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ISRP Style
Alica Miller, Weak mixing in general semiflows implies multi-sensitivity, but not thick sensitivity, Journal of Nonlinear Sciences and Applications, 12 (2019), no. 2, 120--123
AMA Style
Miller Alica, Weak mixing in general semiflows implies multi-sensitivity, but not thick sensitivity. J. Nonlinear Sci. Appl. (2019); 12(2):120--123
Chicago/Turabian Style
Miller, Alica. "Weak mixing in general semiflows implies multi-sensitivity, but not thick sensitivity." Journal of Nonlinear Sciences and Applications, 12, no. 2 (2019): 120--123
Keywords
- Weak mixing
- sensitivity
- multi-sensitivity
- thick sensitivity
- semi-flow
MSC
- 37B05
- 54H20
- 37D45
- 37B20
- 37B99
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