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

24 pages, 8 eps-figuresWe introduce a deterministic model defined on a two dimensional hyperbolic lattice. This model provides an example of a non random system whose multifractal behaviour has a number theoretic origin. We determine the multifractal exponents, discuss the termination of multifractality and conjecture the geometric origin of the multifractal behavior in Liouville quasi--classical field theory