摘要：We study the differentiability properties of the pre-image pressure. For a TDS (𝑋,𝑇) with finite topological pre-image entropy, we prove the pre-image pressure function 𝑃pre(𝑇,•) is Gateaux differentiable at 𝑓∈𝐶(𝑋,ℝ) if and only if 𝑃pre(𝑇,•) has a unique tangent functional at 𝑓. Also, we obtain some equivalent conditions for 𝑃pre(𝑇,•) to be Fréchet differentiable at 𝑓.
