A generalized semiconjugacy in difference equations

Difference equations arise in many fields. This article is concerned to generalization of semiconjugacy in difference equations. In fact, H. Sedaghat in [7] investigated the semiconjugacy in difference equations where the factor maps are one-dimensional. We generalize the definition of semiconjugacy of maps, where the factor map is multi-dimensional. This generalization is very useful. By this generalization, we can investigate the dynamics of many difference equations especially the dynamics of systems of higher order difference equations. Some systems of difference equations are investigated using the semiconjugacy property.