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Analýza a obvodové realizace speciálních chaotických systémů / Analysis and circuit realization of special chaotic systemsRujzl, Miroslav January 2021 (has links)
This master‘s thesis deals with analysis of electronic dynamical systems exhibiting chaotic solution. In introduction, some basic concepts for better understanding of dynamical systems are explained. After introduction, current knowledge from the world of circuits exhibiting chaotic solutions are discussed. The best-known chaotic systems are analyzed numerically in Matlab software. Numerical analysis and experimental verification were demonstrated at C class transistor amplifier, which confirmed the chaotic behavior and generation of a strange attractor.
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C*-algebras from actions of congruence monoidsBruce, Chris 20 April 2020 (has links)
We initiate the study of a new class of semigroup C*-algebras arising from number-theoretic
considerations; namely, we generalize the construction of Cuntz, Deninger,
and Laca by considering the left regular C*-algebras of ax+b-semigroups from actions
of congruence monoids on rings of algebraic integers in number fields. Our motivation
for considering actions of congruence monoids comes from class field theory and work
on Bost–Connes type systems. We give two presentations and a groupoid model for
these algebras, and establish a faithfulness criterion for their representations. We
then explicitly compute the primitive ideal space, give a semigroup crossed product
description of the boundary quotient, and prove that the construction is functorial
in the appropriate sense. These C*-algebras carry canonical time evolutions, so that
our construction also produces a new class of C*-dynamical systems. We classify the
KMS (equilibrium) states for this canonical time evolution, and show that there are
several phase transitions whose complexity depends on properties of a generalized
ideal class group. We compute the type of all high temperature KMS states, and
consider several related C*-dynamical systems. / Graduate
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