Abstract:
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) 7−→ gx. For a family F of
subset of X and A ∈ F, we denote ∆F(A) = {g ∈ G : gB ⊆ A for
some B ∈ F, B ⊆ A}, and say that a subset R of G is F-recurrent
if R
T
∆F(A) 6= ∅ for each A ∈ F.
