Local fields, iterated extensions, and Julia Sets
| dc.contributor.advisor | Manes, Michelle | |
| dc.contributor.author | Lee, Pui Hang | |
| dc.contributor.department | Mathematics | |
| dc.date.accessioned | 2025-09-30T22:32:18Z | |
| dc.date.available | 2025-09-30T22:32:18Z | |
| dc.date.issued | 2025 | |
| dc.description.degree | Ph.D. | |
| dc.identifier.uri | https://hdl.handle.net/10125/111283 | |
| dc.subject | Mathematics | |
| dc.title | Local fields, iterated extensions, and Julia Sets | |
| dc.type | Thesis | |
| dcterms.abstract | Let $K$ be a field complete with respect to a discrete valuation $v$ of residue characteristic $p$, and let $f(z) = z^\ell - c \in K[z]$ be a separable polynomial. We explore the connection between the valuation $v(c)$ and the Berkovich Julia set of $f$. Additionally, we examine the field extensions generated by the solutions to $f^n(z) = \alpha$ for a root point $\alpha \in K$, highlighting the interplay between the dynamics of $f$ and the ramification in the corresponding field extensions. | |
| dcterms.extent | 44 pages | |
| dcterms.language | en | |
| dcterms.publisher | University of Hawai'i at Manoa | |
| dcterms.rights | All UHM dissertations and theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission from the copyright owner. | |
| dcterms.type | Text | |
| local.identifier.alturi | https://www.proquest.com/LegacyDocView/DISSNUM/32120836 |
Files
Original bundle
1 - 1 of 1
Loading...
- Name:
- Lee_hawii_0085A_12690.pdf
- Size:
- 519.92 KB
- Format:
- Adobe Portable Document Format