On recurrence in G-spaces - Protasov, I.V.; Protasova, K.D. (Algebra and Discrete Mathematics, 2017)
We introduce and analyze the following general concept of recurrence. Let G be a group and let X be a G-space with the action G×X⟶X, (g,x)⟼gx. For a family F of subset of X and A∈F, we denote ΔF(A)={g∈G:gB⊆A for some B∈F, B⊆A}, and say that a subset R of G is F-recurrent if R⋂ΔF(A)≠∅ for each A∈F.