Kotova O. Topological, metric and fractal properties of sets of solutions of equations containing fractal functions

In the thesis we examine families of real numbers such that their s-adic representations have some asymptotic or quasiperiodic properties. We study liniar equations which contain functions with complex local structure (function of digit "i" in s-adic representation of x and let f(x) is a continious nowhere differentiable function such that its binary representation determined by ternary representation of x). We also study topological, metrical an fractal properties of sets of real numbers with some conditions on their Q-representation : independence and Markov dependence of digits on the infinite set of positions).