Algebraic independence of local conjugacies and related questions in polynomial dynamics
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Abstract:
Let $K$ be an algebraically closed field of characteristic 0 and $f\in K[t]$ a polynomial of degree $d\geq 2$. There exists a local conjugacy $\psi _f(t)\in tK[[1/t]]$ such that $\psi _f(t^d)=f(\psi _f(t))$. It has been known that $\psi _f$ is transcendental over $K(t)$ if $f$ is not conjugate to $t^d$ or a constant multiple of the Chebyshev polynomial. In this paper, we study the algebraic independence of $\psi _{f_1}$,…,$\psi _{f_n}$ using a recent result of Medvedev and Scanlon. Related questions in transcendental number theory and canonical heights in arithmetic dynamics are also discussed.References
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Additional Information
- Khoa D. Nguyen
- Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
- Address at time of publication: Department of Mathematics, University of British Columbia, and Pacific Institute for the Mathematical Sciences, Vancouver, British Columbia V6T 1Z2, Canada
- Email: khoanguyen2511@gmail.com, dknguyen@math.ubc.ca
- Received by editor(s): October 8, 2013
- Published electronically: December 9, 2014
- Communicated by: Matthew A. Papanikolas
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 1491-1499
- MSC (2010): Primary 11J91, 37F10; Secondary 37P30
- DOI: https://doi.org/10.1090/S0002-9939-2014-12438-5
- MathSciNet review: 3314064