Study of Dynamical System and Topological Transitivity with Ideals

Résumé

This paper will discuss the problem of defining the new type of topological transitivity. To do this several equivalent topological transitivity and non-wandering point has been discussed through this paper. This paper also consider the ideal version of transitivity with the help of the amendment of the result Remark $6.9(2)$ of \cite{LL2013}. Corrected version of the Remark: ``If $\mathcal{\bf I}$ is codense, then $\mathcal{\bf I}$-denseness, $*$-denseness and denseness are equivalent" will be ``If $\mathcal{\bf I}$ is completely codense, then $\mathcal{\bf I}$-denseness, $*$-denseness and denseness are equivalent".