On double period G – inverse shadowing property

Abstract

We consider a new property for G – inverse shadowing , we call it double period G – inverse shadowing. We prove that the composite of any n self mappings has double period G – inverse shadowing if this mapping has this property and the converse is true if mappings is G – expansive and G – chain mixing. The Cartesian product of two mapping also has this property if these two mapping have it , and the convers is true in the G – expansivity mapping. Also, we find that the inverse of the mapping has double period G – inverse shadowing is equivalent to this mapping has this property. Besides, this property is deserved topological G – conjugacey. So, in general, we show that this property is not equivalent to G – inverse shadowing, but we can obtain the property G – inverse shadowing from double period G – inverse shadowing property in G – expansivity mapping. Also, if mapping is G – chain transitive, then G – Inverse Shadowing implies double period G – inverse shadowing.

Subject Classification:

• 37C50
• 37C55

Keywords:

• G – inverse shadowing
• Double period G – inverse shadowing
• G – chain mixing
• G – chain transitive
• topological G – conjugacey