Academic Editor: M. De la Sen
Copyright © 2012 Kesong Yan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We study the differentiability properties of the pre-image pressure. For a TDS with finite topological pre-image entropy, we prove the pre-image pressure function is Gateaux differentiable at if and only if has a unique tangent functional at . Also, we obtain some equivalent conditions for to be Fréchet differentiable at .