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pro vyhledávání: '"Huguin, Valentin"'
Given a number field $\mathbb{K} \subset \mathbb{C}$ that is not contained in $\mathbb{R}$, we prove the existence of a dense set of entire maps $f \colon \mathbb{C} \rightarrow \mathbb{C}$ whose preperiodic points and multipliers all lie in $\mathbb
Externí odkaz:
http://arxiv.org/abs/2304.13674
Let $\mathcal{O}_{K}$ be the ring of integers of an imaginary quadratic field $K$. Recently, Ji and Xie proved that every rational map $f \colon \widehat{\mathbb{C}} \rightarrow \widehat{\mathbb{C}}$ of degree $d \geq 2$ whose multipliers all lie in
Externí odkaz:
http://arxiv.org/abs/2212.03661
Autor:
Huguin, Valentin
In this article, we show that every rational map whose multipliers all lie in a given number field is a power map, a Chebyshev map or a Latt\`{e}s map. This strengthens a conjecture by Milnor concerning rational maps with integer multipliers, which w
Externí odkaz:
http://arxiv.org/abs/2210.17521
Autor:
Huguin, Valentin
In this article, we prove that every quadratic rational map whose multipliers all lie in the ring of integers of a given imaginary quadratic field is a power map, a Chebyshev map or a Latt\`{e}s map. In particular, this provides some evidence in supp
Externí odkaz:
http://arxiv.org/abs/2107.07262
Autor:
Huguin, Valentin
In this article, we prove that every unicritical polynomial map that has only rational multipliers is either a power map or a Chebyshev map. This provides some evidence in support of a conjecture by Milnor concerning rational maps whose multipliers a
Externí odkaz:
http://arxiv.org/abs/2009.02422
Autor:
Huguin, Valentin
In this article, we study the set of parameters $c \in \mathbb{C}$ for which two given complex numbers $a$ and $b$ are simultaneously preperiodic for the quadratic polynomial $f_{c}(z) = z^{2} +c$. Combining complex-analytic and arithmetic arguments,
Externí odkaz:
http://arxiv.org/abs/1906.04514
Akademický článek
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Autor:
Huguin, Valentin1 (AUTHOR)
Publikováno v:
Conformal Geometry & Dynamics. 6/30/2021, Vol. 25, p79-87. 9p.
Autor:
Huguin, Valentin1 valentin.huguin@math.univ-toulouse.fr
Publikováno v:
New York Journal of Mathematics. 2021, Vol. 27, p363-378. 16p.
Let $O_K$ be the ring of integers of an imaginary quadratic field. Recently, Zhuchao Ji and Junyi Xie proved that rational maps whose multipliers at all periodic points belong to $O_K$ are power maps, Chebyshev maps or Latt\`es maps. Their proof reli
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5063c3695844f4990ae0cb6ad3a33b93
http://arxiv.org/abs/2212.03661
http://arxiv.org/abs/2212.03661