On Dynamical System and Topological Transitivity via Ideals

This paper will discuss the problem of defining the new topological transitivity. To do this several equivalent topological transitive 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 $\mathbf{I}$ is completely codense, then $\mathbf{I}$-denseness, $\ast$-denseness and denseness are equivalent".