Now showing items 1-8 of 8

    • Adding machines. 

      Jones, Leslie Braziel. (2009-06-01)
      We explore the endpoint structure of the inverse limit space of unimodal maps such that the restriction of the map to the ω-limit set of the critical point is topologically conjugate to an adding machine. These maps fall ...
    • Asymptotic arc-components in inverse limits of dendrites. 

      Hamilton, Brent (Brent A.) (, 2011-09-14)
      We study asymptotic behavior arising in inverse limit spaces of dendrites. In particular, the inverse limit is constructed with a single unimodal bonding map, for which points have unique itineraries and the critical point ...
    • Chaos in dendritic and circular Julia sets. 

      Averbeck, Nathan, 1985- (2016-07-01)
      We demonstrate the existence of various forms of chaos (including transitive distributional chaos, w-chaos, topological chaos, and exact Devaney chaos) on two families of abstract Julia sets: the dendritic Julia sets DT ...
    • Chaotic properties of set-valued dynamical systems. 

      Tennant, Timothy, 1987- (2016-04-04)
      In this thesis, many classical results of topological dynamics are adapted to the set-valued case. In particular, focus is given to the notions of topological entropy and the specification property. These properties are ...
    • Knot Equivalence Through Braids and Rational Tangles 

      Schultze, Adam (2013-05-23)
      A major goal in the study of knot theory is to discover more practical and universal methods that determine knot equivalence. In this paper, we will explore two methods of doing so through the use of rational tangles and ...
    • Multi-Parameter Functions in Chaotic Dynamical Systems 

      Hollister, Megan (2017-05-24)
      For two semesters, a fellow math major and I thoroughly proved results from Sections 1.1 – 1.8 of An Introduction to Chaotic Dynamical Systems by Robert Devaney. After going through Devaney's calculations and proofs, I ...
    • Orbit structures of homeomorphisms. 

      Sherman, Casey L. (, 2012-11-29)
      In this dissertation we answer the following question: If X is a Cantor set and T: X → to X is a homeomorphism, what possible orbit structures can T have? The answer is given in terms of the orbit spectrum of T. If X is a ...
    • The specification property and chaos in multidimensional shift spaces and general compact metric spaces. 

      Hunter, Reeve. (2016-06-28)
      Rufus Bowen introduced the specification property for maps on a compact metric space. In this dissertation, we consider some implications of the specification property for Zᵈ-actions on subshifts of Ʃ^Zᵈ as well as on a ...