Brolin's theorem for periodic points: speed of convergence for z² + c with c in the main cardioid of the Mandelbrot set
dc.contributor.author | Naeger, Matthew J. | |
dc.date.accessioned | 2020-08-14T16:02:52Z | |
dc.date.available | 2020-08-14T16:02:52Z | |
dc.date.graduationmonth | August | en_US |
dc.date.issued | 2020-08-01 | |
dc.date.published | 2020 | en_US |
dc.description.abstract | Brolin'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 |
dc.description.advisor | Tanya Firsova | en_US |
dc.description.degree | Master of Science | en_US |
dc.description.department | Department of Mathematics | en_US |
dc.description.level | Masters | en_US |
dc.identifier.uri | https://hdl.handle.net/2097/40836 | |
dc.language.iso | en_US | en_US |
dc.subject | Complex dynamics | en_US |
dc.subject | Polynomial iteration | en_US |
dc.subject | Brolin's theorem | en_US |
dc.title | Brolin's theorem for periodic points: speed of convergence for z² + c with c in the main cardioid of the Mandelbrot set | en_US |
dc.type | Thesis | en_US |