  We study stationary, periodic solutions to the thermocapillary thin-film
model
  \begin{equation*}
  \partial_t h + \partial_x \Bigl(h^3(\partial_x^3 h - g\partial_x h) +
M\frac{h^2}{(1+h)^2}\partial_xh\Bigr) = 0,\quad t>0,\ x\in \mathbb{R},
  \end{equation*} which can be derived from the B\'enard-Marangoni problem via
a lubrication approximation. When the Marangoni number $M$ increases beyond a
critical value $M^*$, the constant solution becomes spectrally unstable via a
(conserved) long-wave instability and periodic stationary solutions bifurcate.
For a fixed period, we find that these solutions lie on a global bifurcation
curve of stationary, periodic solutions with a fixed wave number and mass.
Furthermore, we show that the stationary periodic solutions on the global
bifurcation branch converge to a weak stationary periodic solution which
exhibits film rupture. The proofs rely on a Hamiltonian formulation of the
stationary problem and the use of analytic global bifurcation theory. Finally,
we show the instability of the bifurcating solutions close to the bifurcation
point and give a formal derivation of the amplitude equation governing the
dynamics close to the onset of instability.
