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Equations at infinity for critical-orbit-relation families of rational maps
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Ramadas, Rohini and Silversmith, Rob (2022) Equations at infinity for critical-orbit-relation families of rational maps. Experimental Mathematics . doi:10.1080/10586458.2022.2113575 ISSN 1944-950X. (In Press)
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WRAP-Equations-at-infinity-critical-orbit-relation-families-rational-maps-22.pdf - Accepted Version - Requires a PDF viewer. Download (11Mb) | Preview |
Official URL: https://doi.org/10.1080/10586458.2022.2113575
Abstract
We develop techniques for using compactifications of Hurwitz spaces to study families of rational maps from P^1 to P^1 defined by critical orbit relations. We apply these techniques in two settings: We show that the parameter space Per_{d,n} of degree-d bicritical maps with a marked 4-periodic critical point is a d^2-punctured Riemann surface of genus (d−1)(d−2)/2. We also show that the parameter space Per_{2,5} of degree-2 rational maps with a marked 5-periodic critical point is a 10-punctured elliptic curve, and we identify its isomorphism class over Q. We carry out an experimental study of the interaction between dynamically defined points of Per_{2,5} (such as PCF points or punctures) and the group structure of the underlying elliptic curve.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Journal or Publication Title: | Experimental Mathematics | ||||||||
| Publisher: | Taylor & Francis | ||||||||
| ISSN: | 1944-950X | ||||||||
| Official Date: | 2022 | ||||||||
| Dates: |
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| DOI: | 10.1080/10586458.2022.2113575 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | In Press | ||||||||
| Reuse Statement (publisher, data, author rights): | This is an Accepted Manuscript version of the following article, accepted for publication in Experimental Mathematics. Rohini Ramadas & Rob Silversmith (2022) Equations at Infinity for Critical-Orbit-Relation Families of Rational Maps, Experimental Mathematics, DOI: 10.1080/10586458.2022.2113575. It is deposited under the terms of the Creative Commons Attribution-NonCommercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited.” | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 2 September 2022 | ||||||||
| Date of first compliant Open Access: | 3 September 2023 | ||||||||
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| Open Access Version: |
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