Published July 2021
| Accepted Version
Journal Article
Open
Univalent polynomials and Hubbard trees
Abstract
We study rational functions f of degree d+1 such that f is univalent in the exterior unit disc, and the image of the unit circle under f has the maximal number of cusps (d+1) and double points (d−2). We introduce a bi-angled tree associated to any such f. It is proven that any bi-angled tree is realizable by such an f, and moreover, f is essentially uniquely determined by its associated bi-angled tree. This combinatorial classification is used to show that such f are in natural 1:1 correspondence with anti-holomorphic polynomials of degree d with d−1 distinct, fixed critical points (classified by their Hubbard trees).
Additional Information
© 2021 American Mathematical Society. Received by the editors February 12, 2020, and, in revised form, October 4, 2020. Article electronically published on April 28, 2021. The third author was supported by the Institute for Mathematical Sciences at Stony Brook University, an endowment from Infosys Foundation and SERB research grant SRG/2020/000018 during parts of the work on this project. He also thanks Caltech for their support towards the project. The authors thank the anonymous referee for numerous valuable suggestions.Attached Files
Accepted Version - 1908.05813.pdf
Files
1908.05813.pdf
Files
(2.9 MB)
| Name | Size | Download all |
|---|---|---|
|
md5:79b227a5f87e7f0dc992afde722e14e9
|
2.9 MB | Preview Download |
Additional details
- Eprint ID
- 109846
- Resolver ID
- CaltechAUTHORS:20210715-154348375
- Stony Brook University
- Infosys Foundation
- SRG/2020/000018
- Science and Engineering Research Board (SERB)
- Caltech
- Created
-
2021-07-15Created from EPrint's datestamp field
- Updated
-
2021-07-15Created from EPrint's last_modified field