%0 Journal Article
%T A quantitative approach to syndetic transitivity and topological ergodicity
%A Zhao, Yu
%A Li, Risong
%A Lu, Tianxiu
%A Jiang, Ru
%A Wang, Hongqing
%A Liang, Haihua
%J Journal of Nonlinear Sciences and Applications
%D 2017
%V 10
%N 9
%@ ISSN 2008-1901
%F Zhao2017
%X In this paper, we give new quantitative
characteristics of degrees of syndetical transitivity and
topological ergodicity for a given discrete dynamical system, which
are nonnegative real numbers and are not more than \(1\). For selfmaps
of many compact metric spaces it is proved that a given selfmap is
syndetically transitive if and only if its degree of syndetical
transitivity is \(1\), and that it is topologically ergodic if and
only if its degree of topological ergodicity is one. Moreover, there
exists a selfmap of \([0, 1]\) having all degrees positive.
%9 journal article
%R 10.22436/jnsa.010.09.10
%U http://dx.doi.org/10.22436/jnsa.010.09.10
%P 4680--4686