Metrical chaotic properties of G-inverse shadowing property

This paper is concerned with relationships among G-inverse shadowing property, G-expansivity and G-Sensitivity. In the class T_0, G-inverse shadowing does not imply G-expansive. We generalize the concept of eventually sensitive to G-space, and we see that G-inverse shadowing does not imply eventually G-sensitive in the class T_0. On the other hand, G-inverse shadowing with totally G-transitive imply G-sensitive in the class of continuous methods T_c. So, G-sensitive is obtained from G-inverse shadowing and dense set of G-periodic point.