Forward and pullback dynamics of nonautonomous integrodifference equations: Basic constructions

The paper’s Theorem 4.11 states that under uniform asymptotic autonomy on a forward absorbing set A (condition (4.9)), every forward limit fibre Ω_A(τ) equals the global attractor A* of the autonomous limit system, and hence ω−_A = ω+_A = A*; see the statement and assumptions around (4.9) and Theorem 4.11. This matches the candidate’s conclusion precisely. The paper proves Ω_A(τ) = A* by comparing directly to A* via attraction and a triangle-inequality argument, while the model first identifies ω_F(A) with A* and then shows Ω_A(τ) = ω_F(A); both routes are valid. A minor convention issue: the model discusses the closed/Kuratowski version of Ω_A(τ), whereas the paper defines Ω_A(τ) without inner closures but still obtains equality with A* under the stated hypotheses. Overall, both are correct, using slightly different but compatible proofs.