Benford's law in Deterministic Processes

Benford’s Law describes how leading digits of numbers are distributed among a large amount of data sets. Intuitively it seems reasonable to assume that numbers follow a uniform distribution, instead they follow a particular logarithmic distribution. For example, the number 1 appears as the first digit approximately 30,6% of the times, while the number 9 occurs less than 5% of the times. In this thesis I am going to discuss about the Real-Valued Deterministic Processes and their connection with Benford’s law. A one-dimensional deterministic process is a system in which there is no randomity that affects the future states of the system itself and for that is one of the simplest models for evolving processes. In mathematics these models are described by one-dimensional differential equations and the purpose of this thesis is to study under what conditions they conform to Benford’s law.