Brett Bozyk

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This paper is a study of special families of rational maps of the real plane of the form: z → z n + c + β/z d , where the dynamic variable z ∈ C, and C is identified with R 2. The parameters c and β are complex ; n and d are positive integers. For β small, this family can be considered a non-holomorphic singular perturbation of the holomorphic family z → z(More)
In this paper we explore an area of dynamical systems that we call non-analytic continuations of analytic maps. These could have many forms, but we are interested in: F β,c (z) = z n + c + β z d , where c, β ∈ C, z is the complex conjugate of z ∈ C orˆC, and n, d ∈ N. We are particularly interested in the case c = 0 with n = d. When viewed as a map of the(More)
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