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Creators/Authors contains: "Ismert, Lara"

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  1. ; ; ; (, Ball State Undergraduate Mathematics Exchange)
    Both the Mandelbrot set and filled Julia sets are subsets in the complex plane derived by studying iterations of complex polynomials. We develop a matricial framework to establish an alternate form of iteration by complex polynomials using a sequence of affine transformations. Using this framework, we are able to check membership in a filled Julia set and the Mandelbrot set by studying boundedness of sequences of matrices. Specifically, we show that a complex number belongs to the Mandelbrot set if and only if a particular sequence of matrices is bounded in the operator norm, and a complex number belongs to a filled Julia set if and only if a particular sequence of matrices is bounded in operator norm. 
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  2. ; ; ; ; (, Journal of the London Mathematical Society)
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