Abstract/Details

Enveloping semigroups of affine skew products and Sturmian-like systems

Pikula, Rafal.   The Ohio State University ProQuest Dissertations Publishing,  2009. 3375785.

Abstract (summary)

Let (X, Γ) be a topological dynamical system, meaning that X is a compact Hausdorff space, and Γ is a group of continuous maps from X to itself. The enveloping semigroup E(X, Γ) of the system (X, Γ) is defined to be the closure of Γ in XX equipped with the product topology. We consider distal actions of groups generated by uinpotent affine transformations on a finite dimensional torus and we investigate the structure of the arising enveloping semigroup. It is known that in this case the enveloping semigroup is a group. We show that this group is necessarily nilpotent and find bounds on its nilpotency class. Moreover, if Γ is generated by a single transformation T of the aforementioned form we are able to determine precisely how the nilpotency class depends on T.

We also compute the enveloping semigroups of Sturmian and Sturmian-like systems enlarging the collection of existing explicit computations of these objects.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Affine skew products; Enveloping semigroups; Skew products; Sturmian-like systems
Title
Enveloping semigroups of affine skew products and Sturmian-like systems
Author
Pikula, Rafal
Number of pages
132
Degree date
2009
School code
0168
Source
DAI-B 70/10, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
978-1-109-41458-5
Advisor
Bergelson, Vitaly
University/institution
The Ohio State University
Department
Mathematics
University location
United States -- Ohio
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3375785
ProQuest document ID
304967098
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/304967098