  Using the work of Bonahon-Dreyer and Fock-Goncharov, one can construct a
real-analytic parameterization for the PSL(n,R) Hitchin component of a surface
S, that is explicitly analogous to the Fenchel-Nielsen coordinates on the
Teichmuller space of S. Given a Hitchin representation, we give a lower bound
on the "length" of any closed curve on S in terms of the parameters describing
this representation. We then show that this lower bound is good enough to
produce large families of sequences in the Hitchin component along which the
topological entropy converges to 0.
