Oliver Schmitt
Remarks on the Generator-Problem
Preprint series: Mathematica Gottingensis

MSC:

28D05 Measure-preserving transformations

37A05 Measure-preserving transformations

ZDM: I50
Abstract: The existence and structure of generators for endomorphisms
are investigated in the setup of classical as well as of
relative ergodic theory. We present an explicit
construction of a finite one-sided generator for aperiodic
automorphisms with zero entropy. In the case of positive
entropy, we demonstrate the complexity of this task by
discussing an important example. Moreover, we provide a
generalisation of the Abramov-Rohlin-formula and prove
the existence of one-sided relative generators with finite
entropy.

Keywords: one-sided generator, rokhlin tower, relative entropy
Notes: Part I