Naeger, Matthew J.2020-08-142020-08-142020-08-01https://hdl.handle.net/2097/40836Brolin's theorem states that for a monic polynomial f on the complex plane of degree d greater than or equal to 2, for a non-exceptional point a, the backwards orbit of a equidistributes on the Julia set of f [1]. Tortrat [9] proved a version of Brolin's theorem for periodic points. Drasin and Okuyama [3] proved a rate of convergence result for Brolin's theorem, and we use some of their work to prove a similar result for the periodic version of Brolin's theorem whenever f is a quadratic polynomial with parameter c in the main cardioid of the Mandelbrot set.en-US© the author. This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).http://rightsstatements.org/vocab/InC/1.0/Complex dynamicsPolynomial iterationBrolin's theoremThesis