Dissertation

Measures and Matching for Number Systems

Author: Maggioni, M.
Date: 04 March 2021
Links: Thesis in Leiden University Scholarly Publications

This thesis provides explicit expressions for the density functions of absolutely continuous invariant measures for general families of interval maps, that include random maps and infinite measure transformations, not necessarily number systems. Natural extensions, the Perron-Frobenius operator and the dynamical phenomenon of matching are some of the techniques exploited to obtain such results. In particular, in this thesis the notion of matching is for the first time recognised in an infinite measure system and the definition, known so far for deterministic transformations only, is extended to cover random interval maps as well. The thesis also presents new developments in the area of number expansions