Multifractality in uniform hyperbolic lattices and in quasi-classical Liouville field theory

We introduce a deterministic model defined on a two dimensional hyperbolic lattice. This model provides an example of a non random system whose multif ractal behaviour hus a number theoretic origin. We determine the multifract al exponents, discuss the termination of multifractality and conjecture the geometric origin of the multifractal behavior in Liouville quasi-classical field theory.