Let q be a prime power, and let 𝔽_q be the finite field of order q. For a polynomial φ ∈ 𝔽_q[X], let d_{n,φ}(X) denote the denominator of the n-th iterate of 1/φ(X). We call φ inversely stable if the polynomials d_{n,φ} are pairwise distinct and irreducible over 𝔽_q for all n ≥ 1. In this talk, we shall report some progress on the inverse stability of linearized polynomial over 𝔽_q.