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


Alica Miller - Department of Mathematics, University of Louisville, USA.


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.