Here are some questions about the earthquake deformation of hyperbolic surface that I can't answer or find references.

I briefly recall the settings. Let's fix a closed surface $S$ with genus $g\geq 2$. A point $h$ in the Teichmuller space $\mathscr{T}$ of $S$ may be thinked of
either (a) as a marked hyperbolic structure on $S$

or
(b) as a conjugate class of representations $\pi_1(S)\rightarrow PSL(2,\mathbb{R})$.

For any simple closed curve $\alpha$ on $S$, the Fenchel-Nielson twist along $\alpha$ gives rise to a flow $\phi_\alpha^t$ on $\mathscr{T}$. Wolpert proved that $\phi_\alpha^t$ is an Hamiltonian flow with respect to the Weil-Petersson symplectic structure. We can describe the deformation in the representation level. Namely, take a representation $h:\pi_1(S)\rightarrow PSL(2,\mathbb{R})$ which defines a point in $\mathscr{T}$, if $\alpha$ is seperating, then $\pi_1(S)$ is the amalgamated product of two groups, and $\phi_\alpha^t(h)$ is a representation in which we modify restriction of $h$ on one of the two groups by conjugation.

Thurston's eathquake deformation is a generalization of the above construction where we take a geodesic lamination instead of simple closed curve.

**Question 1**: Is there any example of an explicit family of representations $h_t:\pi_1(S)\rightarrow PSL(2,\mathbb{R})$ which gives an earthquake deformation supported on some non-simple lamination?

**Question 2**: Is the earthquake flow Hamiltonian, say, generated by the "generalized length function" of laminations?

**Question 3**: Can one describe the limit of $\phi_\alpha^t(h)$, as a projectived measured lamination, when $t\rightarrow\pm\infty$ (at least when $\alpha$ is simple closed)? For example, is it a measured lamination supported on $\alpha$?

**Remark to question 3**: I'm not sure of this, it seems that the review of a paper of Bonahon suggests $\phi_\alpha^t$ extends to a non-trivial action on the Thurston boundary of $\mathscr{T}$. If it is true, then the limit in question 3 does not always exist.

**Addendum**: Now I realized that I made some conceptual mistakes about **Question 3**. Once we think of the earthquake flow intuitively as "horocycle flow" like on the upper half plan, the picture would be clear.