Browsing by Subject "Chaos"

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    Newton's Method For A Non-Analytical Perturbation of Z^2-1
    (2020-06) Wong, Noah
    This paper aims to analyze the discrete dynamical system arising from New-ton’s method applied to the two-dimensional real quadratic polynomial given by the analogue of the complex function H_A(z) =z^2−1 +A ̄z with complex parameter A. This equation derives from a perturbation of the well known system of Newton’s method for F(z) =z^2−1. The complex dynamics for Newton’s method applied to F have many of the same properties as the perturbation. We use these properties to analyze and describe the orbits for our system. Then by restricting our parameter value A=a+bi we were able to fully describe the dynamics for when |a| < 2/(3√3), b= 0 and partially describe the dynamics for when a= 0, |b|<2. A key result is the existence of an invariant line on which the Newton map is topologically conjugate to the doubling map. The doubling map is D: [0,1)→[0,1), with D(x) = 2x(mod 1). We use results from this map to describe our system. We present conjectures to describe the behavior of orbits in both cases. Finally we present some preliminary results for the dynamics of the system for parameter values not in those two cases.
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    Nouvelles dramaturgies africaines francophones du chaos
    (2014-12) Ngilla, Sylvie Ndome
    A new type of African Francophone theater has emerged since the 1990s, which announced a breaking point within the African literary landscape. This generation of contemporary writers from the African diaspora engages with notions of fragmentation, displacement, and instability that suggest a reconfiguration of chaos in Francophone African literary production since the Independences. The history of African literatures since 1960, when a large majority of former African colonies became independent, is marked by the theme of chaos with significant differences. Indeed, between 1960 and 1970, writers of the « disenchantment » denounce social and political chaos in Africa following the emergence of new dictatorships in the post-independence period. African theatrical aesthetics by the end of the 1970s and through the 1980s, on the contrary, work on an exit out of the African chaos from the perspective of revalorization, providing modern contextualizations for African myths and traditions. Since the early 1990s a rupture is established within new African theater that creates a performative space of « chaos-monde », which manifests the hybrid reality of the African diaspora at local and global levels. By reading across theatrical works by this generation that include Caya Makélé (Congo), Koffi Kwahulé (Ivory Coast), Marcel Zang (Cameroon), José Pliya (Benin), Kossi Efoui (Togo), and Dieudonné Niangouna (Congo), I shed light on the new techniques and aesthetics of an energetic chaos. A close examination of these new settings of chaos allows for a better understanding of the diasporic nature and transnational perspective from contemporary African theater.