On the ϵ-Entropy of Nearly Critical Values Original Research Article

Let ƒ be a Ck-mapping into Rm, restricted to a compact subset of Rn. We compute an upper bound on the ϵ-entropy of the nearly critical values. This refines some results of Yomdin. The bound depends only on dimensions, the differentiability degree k, and estimates of the norms of the first and kth derivative of ƒ.