Geodesic length spectrum on compact Riemann surfaces

In this paper we use techniques linking combinatorial structures (symbolic dynamics) and algebraic-geometric structures to study the variation of the geodesic length spectrum, with the Fenchel-Nielsen coordinates, which parametrize the surface of genus τ = 2. We explicitly compute length spectra, for all closed orientable hyperbolic genus two surfaces, identifying the exponential growth rate and the first terms of growth series