On Sufficient Conditions for Chaotic Behavior of Multidimensional Discrete Time Dynamical System

Abstract In this work, we look at the extension of classical discrete dynamical system to multidimensional discrete-time by characterizing chaos notions on $${\mathbb {Z}}^d$$ Z d -action. The -action a space X has been defined in very general manner, and therefore introduce which is induced continuous map, $$f:{\mathbb {Z}}\times \rightarrow X$$ f : × X → denotes it as $$T_f:{\mathbb {Z}}^d \times T . Basically, wish relate behavior origin systems ( , f ) its $$(X,T_f)$$ ( , ) chaotic behaviors that emphasized are transitivity dense periodicity property. Analogues these notions, consider k -type property system. process, obtain some conditions under inherited from original ). varies whenever open, totally transitive or mixing. Some examples given illustrate conditions.