Measures and matching for number systems

Maggioni, M. (2021)

Doctoral Thesis

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

• Interval map
• Invariant measure
• Number system
• Number expansion
• Matching
• Natural extension

• All authors: Maggioni, M.
• Supervisor: Hollander, W.T.F. den; Kalle, C.C.C.J.
• Committee: Duijn Schouten, F.A. van der; Merks, R.H.M.; Bahsoum, W.; Homburg, A.J.; Pelantova, E.
• Qualification: Doctor (dr.)
• Awarding Institution: Mathematical Institute (MI), Faculty of Science, Leiden University
• Date: 2021-03-04