3 problems

Let $f$ be an analytic Anosov diffeomorphism of a compact surface, and let $H$ be an analytic function on the surface whose zero level set has no critical points. Conditional measu…

Let $f(x,y)=(1+y-a|x|,bx)$ be a Lozi map with parameters $(a,b)$ in the chaotic regime described above, and let $\rho(\cdot\mid x_0)$ denote the conditional SRB measure on the leve…

Let $(X_v,Y_v)_{v\in\mathbb{Z}^2}$ be a hidden Markov field with $E=F=\{-1,1\}$. Suppose … where $(\xi_v)_{v\in\mathbb{Z}^2}$ are independent and identically distributed, independe…