Leiden University Student Repository

Huiszoon, Leon (2026)

Invariant MeasuresUsingYoungTowers

Master thesis | Mathematics (MSc)

In discrete dynamical systems invariant measures are frequently used to describe long-term behaviour. Here, invariant probability measures absolutely continuous with respect to some natural reference measure, so called acips, are of special interest. We shall use Young Towers to see how for a class of non-uniformly expanding dynamical systems we can find an acip. We show this by using a naturally emerging Polish Space structure and apply a `measure-theoretical version' of Arzelà-Ascoli. Moreover, we shall study random dynamical systems using Random Young Towers, highlight some paradoxes in the existing literature and give conditions for the existence of an acip.

Young Towers, Invariant Measures, Random Dynamical Systems

Author

Huiszoon, Leon

Faculty

Faculty of Science

Supervisors

Kalle, C.C.C.J.
Gaans, O.W. van

ECTS Credits

40

Language

en