 Even for infinitely differentiable maps formula_7, the homeomorphism formula_18 need not to be smooth, nor even locally Lipschitz.However, it turns out to be Hölder continuous, with an exponent depending on the constant of hyperbolicity of formula_19.The Hartman–Grobman theorem has been extended to infinite-dimensional Banach spaces, non-autonomous systems formula_20 (potentially stochastic), and to cater for the topological differences that occur when there are eigenvalues with zero or near-zero real-part.