entropy of geodesic flows on subspaces of hecke surface with arithmetic code

There are di erent ways to code the geodesic ows on surfaces with negative curvature. such code spaces give a useful tool to verify the dynamical properties of geodesic ows. here we consider special subspaces of geodesic ows on hecke surface whose arithmetic codings varies on a set with in nite alphabet. then we will compare the topological complexity of them by computing their topological entropies.