We study Borel complexity of normal numbers in various numeration systems. Taking a dynamical point of view, we can present a unified treatment for base b (b - an integer), beta (beta>1), and continued fraction expansions. At the same time, we obtain analogous results for generic points of invariant measures of dynamical systems of hyperbolic type. In particular, we solve an open problem posed by Sharkovsky. The key dynamical property we need is an appropriate form of specification. The talk is based on a joint work with D. Airey, S. Jackson and W. Mance.
Some complexity results in the theory of normal numbers