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Bounded heights in families of dynamical systems Nguyen, Dang Khoa
Description
Let $a,b\in\bar{\mathbb{Q}}$ be such that exactly one of $a$ and $b$ is an algebraic integer, and let$f_t(z)=z^2+t$be a family of quadratic polynomials parametrized by $t\in\bar{\mathbb{Q}}$. We prove that the set of all $t\in\bar{\mathbb{Q}}$ for which there exist $m,n\geq 0$ such that $f_t^m(a)=f_t^n(b)$ has bounded height. This is a special case of a more general result supporting a new bounded height conjecture in arithmetic dynamics. This is joint work with DeMarco, Ghioca, Krieger, Tucker, and Ye.
Item Metadata
Title |
Bounded heights in families of dynamical systems
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2018-05-12T10:51
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Description |
Let $a,b\in\bar{\mathbb{Q}}$ be such that exactly one of $a$ and $b$ is an algebraic integer, and let$f_t(z)=z^2+t$be a family of quadratic polynomials parametrized by $t\in\bar{\mathbb{Q}}$. We prove that the set of all $t\in\bar{\mathbb{Q}}$ for which there exist $m,n\geq 0$ such that $f_t^m(a)=f_t^n(b)$ has bounded height. This is a special case of a more general result supporting a new bounded height conjecture in arithmetic dynamics. This is joint work with DeMarco, Ghioca, Krieger, Tucker, and Ye.
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Extent |
32.0
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Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Calgary
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Series | |
Date Available |
2019-03-12
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0376825
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Researcher
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International