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Periodic Points And Surfaces Given By Trace Maps, Kevin Gregory Johnston

Theses and Dissertations

In this thesis, we consider the properties of diffeomorphisms of R3 called trace maps. We begin by introducing the definition of the trace map. The group B3 acts by trace maps on R3. The first two chapters deal with the action of a specific element of B3,called αn. In particular, we study the fixed points of αn lying on a topological subspace contained in R3, called T . We investigate the duality of the fixed points of the action ofαn, which will be defined later in the thesis.Chapter 3 involves the study of the fixed points of an element called …