MULTIFRACTAL ANALYSIS OF GENERALISED TAKAGI FUNCTIONS ON THE REAL LINE (Integrated Research on the Theory of Random Dynamical Systems)

Abstract

We investigate the random iteration of finitely many expanding mathscr{C}^{1+varepsilon} diffeomorphisms on the real-line without a common fixed point. We derive the spectral gap property of the associated transition operator on Hölder spaces. As an application we introduce generalised Takagi functions on the real-line and investigate their regulanty properties by means of the pointwise Hölder exponents of these functions.