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 {LL2013}. Corrected version of the Remark: ``If I is codense, then I-denseness, $*$-denseness and denseness are equivalent" will be ``If I is completely codense, then I-denseness, $*$-denseness and denseness are equivalent".