I've recently begun doing research involving pseudo-Anosov diffeomorphisms, which are diffeomorphisms on surfaces $f : M \to M$ admitting two singular measured foliations $(\mathcal F^s, \nu^s)$ and $(\mathcal F^u, \nu^u)$. Frequently I've seen the following notation and I'm having trouble understanding it: $$ f(\mathcal F^s, \nu^s) = (\mathcal F^s, \nu^s/\lambda) \quad \textrm{and} \quad f(\mathcal F^u, \nu^u) = (\mathcal F^u, \lambda \nu^u) $$ for some $\lambda > 1$. In this context, both $\mathcal F^s$ and $\mathcal F^u$ are foliations with the same (finite) set of singularities $S$, and $\nu^s$ and $\nu^u$ are transverse measures to the leaves of $\mathcal F^s$ and $\mathcal F^u$. In particular, if there's a coordinate chart $\phi : U \to \mathbb C$, with $U \subset M$ not containing any singularities, then the leaves of $\mathcal F^s$ and $\mathcal F^u$ are mapped to sets of the form $$\{z : \mathrm{Re}(z) = \mathrm{const}\} \cap \phi(U) \quad \textrm{and} \quad \{z : \mathrm{Im}(z) = \mathrm{const}\} \cap \phi(U)$$ respectively, and $\nu^s|_U$ and $\nu^u|_U$ are pullbacks of $|\mathrm{Re}(dz)|$ and $|\mathrm{Im}(dz)|$. A similar formula (with powers of complex variables) holds in coordinate neighborhoods with singularities.
What I don't understand: These pullback expressions imply if $\gamma$ is a plaque of $\mathcal F^s$, then since $\nu^s(\gamma) = 0$, we must have $\nu^u(\gamma) > 0$. Previously I had interpreted the notation $f(\mathcal F^u, \nu^u) = (\mathcal F^u, \lambda \nu^u)$ to mean that $\nu^u(f(\gamma)) = \lambda \nu^u(\gamma)$, for our $\lambda > 1$. However, in every paper on pseudo-Anosov maps I've read, it's clear that points in the same $\mathcal F^s$-leaf uniformly contract and points in the same $\mathcal F^u$-leaf uniformly expand, which is in direct contradiction to my interpretation. In particular, the exact opposite appears to be the case: $\nu^u(f(\gamma)) = \nu^u(\gamma)/\lambda$ for plaques of $\mathcal F^s$ and $\nu^s(f(\gamma)) = \lambda \nu^s(\gamma)$ for plaques of $\mathcal F^u$.
Can someone explain what the notation $f(\mathcal F^u, \nu^u) = (\mathcal F^u, \lambda \nu^u)$ and $f(\mathcal F^s, \nu^s) = (\mathcal F^s, \nu^s/\lambda)$ means? If points in the same stable leaf of $\mathcal F^s$ are uniformly contracting w.r.t. $\nu^u$ (which is obviously the case in regular Anosov systems) and in the unstable leaf are uniformly expanding w.r.t. $\nu^s$, why do we write $f(\mathcal F^s, \nu^s) = (\mathcal F^s, \nu^s/\lambda)$ and $f(\mathcal F^u, \nu^u) = (\mathcal F^u, \lambda \nu^u)$?
