A Lyapunov exponent associated to modular functions

We define and prove properties of a GL(2, Z)-invariant function, a Lyapunov exponent associated to the modular function j, generalizing a function defined by Spalding and Veselov in the case of the constant function 1. Our results were motivated by conjectures of Kaneko about the "values" of j at real quadratic irrationalities. This is joint work with Paloma Bengoechea and Özlem Imamoglu.