Vasylenko N. Fractal properties of continuous nowhere monotonic and non-differentiable functions

The thesis is devoted to continuous on nowhere monotonic and non-differentiable functions defined by automata with finite memory (transducers of digits of representation for numbers). We study their local and global properties: structural, extremal, differential, integral and fractal properties etc. We consider three families of functions generalizing the known nowhere differentiable functions: Sierpiski function, Takagi (van der Waerden) function, and Trybin (Bush, Wunderlich) function. All generalizations are obtained by use of Q*- and Q-representations of real numbers instead of classic s-adic representation with continuity and nowhere monotonicity preservation.