While routinely used in other areas of dynamics, image sets are ill-defined objects in general
non-invertible measurable dynamics. We propose a way of consistently working with image
sets of null-preserving (and hence, in particular, of measure-preserving) maps. This concept
is illustrated in the context of basic ergodic properties like recurrence, ergodicity, exactness
and existence of generators. It allows us to turn various suasive but logically false statements
about set-theoretic images into actual theorems, and to eliminate extra assumptions on the
measurability of images from some classical results. I will also discuss an application in which
the above is used to significantly improve known results on the abundance of invariant measures
in dissipative systems. (This last application is from joint work with Max Thaler).
Image sets in measurable dynamics
12.10.2023 15:00 - 17:00
Organiser:
H. Bruin, R. Zweimüller
Location: