Analogues of Takens’ theorems for generalized actions of the group ℤ∞

Abstract

The notion of a generalized action of the group ℤ^∞ on a topological space generated by an arbitrary countable family of pairwise commuting homeomorphisms is introduced, and a study of generalized orbits under such actions is given. Analogues of Takens’ theorems on the genericity of the maximal and minimal ɛ-equivalences for such actions are obtained.