Differentiability Properties of the Pre-Image Pressure

الملخص EN

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.