Cantor Minimal Systems and Dimension Groups
AuthorLuciano, Cyrus Anthony
AdvisorBlackadar, Bruce E
StatisticsView Usage Statistics
The theory of general dynamical systems evolved originally in the context of modeling movement in physical systems. Consequently, traditional dynamics is viewed through the lens of differential and difference equations using notions such as state space, trajectory and attractors. Topological dynamics is a generalization and abstraction of these concepts in the context of topological spaces and homeomorphisms. Dimension groups provide a classification up to strong orbit equivalence of minimal Z^d-actions on a Cantor set. The range of such dimension groups for d>1 is still an open question. It appears as if symbolic dynamical systems may be a fruitful approach to this question. In this work, the relationship is explored between Cantor minimal systems, symbolic dynamical systems and dimension groups using properly ordered Bratteli diagrams and their associated Bratteli-Vershik systems. In order to illustrate this relationship we develop the examples of general odometer systems and irrational rotations on the Cantorized circle. Both the K_0 and K^0 groups are calculated using Bratteli diagrams and directed graphs, respectively. Furthermore, the substitution dynamical system associated to a specified irrational rotation is identified showing the method by which one may move between Cantor minimal systems and symbolic dynamical systems.
Showing items related by title, author, creator and subject.
Origins of Ret Signaling in Development of the Insect Gut Nervous System: A Model for Enteric Nervous System Development Myers, Logan Geoffrey (2017)Understanding the evolutionary origins of neurotrophic signaling guiding the formation and upkeep of the central and peripheral nervous systems (CNS/PNS), can offer insights into the basis of development and congenital ...
Implications of the Basque Bilingual Education System: Informing the Establishment of a Kurdish Bilingual Education System in Turkey Ozfidan, Burhan (2012)The Kurdish people have historically occupied the eastern and southeastern regions of Turkey. Since 1923 the Kurdish question is still the most serious internal issue in the Turkish republic's eighty-eight year history. ...
Jafarzadeh, Saeed (2012)In this dissertation, we propose a new approach for the stability analysis of discrete-time and continuous-time, type-1 and type-2 Takagi-Sugano-Kang (TSK) fuzzy systems. A major advantage of the new exponential stability ...