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  • Arithmetic dynamical questions with local rationality conditions

    Creator:
    Noytaptim, Chatchai
    Abstract:
    We introduce a numerical criterion which allows us to bound the degree of any algebraic integer having all of Galois conjugates in an interval of length less than 4. Using this criterion, we study two arithmetic dynamical questions with local rationality conditions. First, we classify all unicritical polynomials defined over...
    Resource Type:
    Dissertation
    Full Text:
    ) ∈ K[x] of degree d > 1. For a dynamical system f ∶ K → K, we usually denote by fn, the n-fold

  • A Ross-Macdonald Model with Vector Demography

    Creator:
    Reyes Grimaldo, Ricardo Noe Gerardo
    Abstract:
    Malaria is a vector-borne disease that has affected humans and other animals for a long time and which has shown high prevalence among different populations. During the beginning of the 20th century, Sir Ronald Ross and George Macdonald developed a model that represents the spread of malaria through the interaction...
    Resource Type:
    Masters Thesis
    Full Text:
    ) is a persistent dynamical system when R0 > 1. Persistence is an important notion in the study of

  • Localized Structures in a Diffusive Run-and-Tumble Model of Myxococcus xanthus

    Creator:
    Flynn, Patrick Thomas
    Abstract:
    The bacteria Myxococcus xanthus clusters into fruiting bodies in the absence of food. The movement of M. xanthus has three aspects: self-propulsion (run), change of direction due to collision (tumble), and Brownian fluctuations in movement. We propose a minimalist PDE model for the concentrations of left and right moving agents...
    Resource Type:
    Honors College Thesis
    Full Text:
    stationary solutions to this equation, utilizing geometry and dynamical systems theory to show existence of

  • Triangular billiards surfaces and translation covers

    Creator:
    Schmurr, Jason Peter
    Abstract:
    We identify all translation covers among triangular billiards surfaces. Our main tools are the J-invariant of Kenyon and Smillie and a property of triangular billiards surfaces, which we call fingerprint type, that is invariant under balanced translation covers.
    Resource Type:
    Dissertation
    Full Text:
    � . Treatments of su h a dynami al system go ba k at least to G.D. Birkho� in 1927[2℄. Fox and Kershner [5℄ des