Universal families and hypercyclic operators

A survey has been done to prove that the principle of universality is a generic phenomenon in analysis. It has been believed that any irregularly behaving process in analysis is capable of producing a universal element. Universality was first observed in 1914 by Fekete. His studies showed that there exists a real power series that only diverges at every point. Thus, ot every continuous function g on [-1,1] with g(0)=0 there exists an increasing sequence of integers.