Abstract
We 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.
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Comtet, A., Nechaev, S. & Voituriez, R. Multifractality in Uniform Hyperbolic Lattices and in Quasi-Classical Liouville Field Theory. Journal of Statistical Physics 102, 203–230 (2001). https://doi.org/10.1023/A:1026568810945
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DOI: https://doi.org/10.1023/A:1026568810945