|
|||||
 |
|
|
|
|
|
|
|
New normal
forms for degree-3 polynomials and rational functions
Heidi Benham, Alexander Galarraga, Benjamin Hutz, Joey Lupo, Wayne Peng and Adam Towsley |
|
Vol. 16 (2023), No. 4, 605–620
|
Abstract |
|
When studying families in the moduli space of dynamical systems, choosing an appropriate representative function for a conjugacy class can be a delicate task. The most delicate questions surround rationality of the conjugacy class compared to rationality of the defining polynomials of the representation. We give a normal form for degree-3 polynomials which has the property that the set of fixed points is equal to the set of fixed point multipliers. This normal form is given in terms of moduli space invariants and, hence, has nice rationality properties. We further classify all degree-3 rational maps which can be conjugated to have a similar relationship between the fixed points and the fixed point multipliers. |
Keywords
dynamical system, normal form, moduli space
|
Mathematical Subject Classification
Primary: 37P05, 37P45
Secondary: 37P15
|
Milestones
Received: 28 April 2022
Revised: 20 October 2022
Accepted: 27 October 2022
Published: 31 October 2023
Communicated by Amanda Folsom
|
Authors |
| Heidi Benham | |
| Department of Mathematics Western Oregon University Monmouth, OR United States |
|
| Alexander Galarraga | |
| Department of Mathematics University of Washington Seattle, WA United States |
|
| Benjamin Hutz | |
| Department of Mathematics and
Statistics Saint Louis University St.Louis, MO United States |
|
| Joey Lupo | |
| Department of Mathematics and
Statistics Amherst College Amherst, MA United States |
|
| Wayne Peng | |
| Department of Mathematics University of Rochester Rochester, NY United States |
|
| Adam Towsley | |
| School of Mathematical
Sciences Rochester Institute of Technology Rochester, NY United States |
|
| © 2023 MSP (Mathematical Sciences Publishers). |
