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Enveloping semigroups of affine skew products and Sturmian-like systems
Pikula, Rafal

2009, Doctor of Philosophy, Ohio State University, Mathematics.

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.

Vitaly Bergelson (Advisor)
Manfred Einsiedler (Committee Member)
Alexander Leibman (Committee Member)
125 p.

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Pikula, R. (2009). Enveloping semigroups of affine skew products and Sturmian-like systems. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Pikula, Rafal. "Enveloping semigroups of affine skew products and Sturmian-like systems." Electronic Thesis or Dissertation. Ohio State University, 2009. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Pikula, Rafal "Enveloping semigroups of affine skew products and Sturmian-like systems." Electronic Thesis or Dissertation. Ohio State University, 2009. https://etd.ohiolink.edu/

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