Recursive set constructions and iterated function systems. Separation conditions and dimension (Q2786193)

This report is a summary of the thesis of the author, it consists of five parts: First section, an introduction, tells us that the main objective is to study different separation conditions on various Moran constructions. A main tool is a simplified version of so called thermodynamic formalism which associates the concept of pressure with the dimension of a dynamically constructed set. Section 2 offers some setting and basic notions. Section 3 is ``pressure''. Section 4 gives measures on the symbol space and derivative of the pressure. Finally, Section 5 contains the separation conditions and dimension results. Moreover, three articles by the author and co-authors are included, namelyNEWLINENEWLINE1. \textit{A. Käenmäki} and \textit{M. Vilppolainen}, Fundam. Math. 200, No.~1, 69--100 (2008; Zbl 1148.28007);NEWLINENEWLINE2. \textit{A. Käenmäki} and \textit{M. Vilppolainen}, Monatsh. Math. 161, No.~3, 271--293 (2010; Zbl 1206.28013) and the paperNEWLINENEWLINE3. ``Weakly controlled Moran constructions and iterated function systems in metric spaces'', with \textit{T. Rajala}, \url{arXiv:1003.0349.210}.