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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Complexity of classification problems in ergodic theory
 Vaněček, Ondřej ; Zelený, Miroslav (advisor) ; Doucha, Michal (referee)
In the thesis we acquaint ourselves with the terms from ergodic theory and re- presentation theory of topological groups. We pay attention particularly to terms unitary representation, realizability by an action, dual group, unitary equivalence and Kazhdan's property (T). We achieve a result regarding unitary representati- ons realizable by an action on finite abelian groups according to article [5] and show that it is possible to generalize it to all finite groups at the end of the thesis according to article [6]. A large part of the text subsequently deals with proper- ties of unitary representations and their relations. We connect the terms compact topological group and Kazhdan's property (T).
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Hausdorff dimension of certain sets
 Vaněček, Ondřej ; Zelený, Miroslav (advisor) ; Spurný, Jiří (referee)
In the thesis we pursue the term Hausdorff measure and dimension. Hausdorff measure is a non-negative quantity, which in a certain way distinguishes among sizes of sets. Using it we define the term Hausdorff dimension, which is useful at studying fractals. These are distinct from other sets by the value of their dimen- sion. By an example of Cantor set we demonstrate the existence of sets, whose dimension in not an integer. Afterwards, we construct a complex theory on the basis of the defined terms, according to which we reach a simple formula allowing us to estimate Hausdorff dimension using an easier method. In conclusion we pay attention to another fractal, Koch curve.
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