Uniform tail entropy for real analytic maps

Let M   be a compact real analytic manifold of finite dimension. There is a function a:(0,+∞)→[0,+∞)a:(0,+∞)→[0,+∞) with limt→0⁡a(t)=0limt→0⁡a(t)=0 such that the tail entropy h⁎(f,ε)h⁎(f,ε) of any real analytic map f on M   is uniformly bounded above by the scale a(ε)a(ε).