Lower bound for the Perron–Frobenius degrees of Perron numbers

Using an idea of Doug Lind, we give a lower bound for the Perron–Frobenius degree of a Perron number that is not totally real, in terms of the layout of its Galois conjugates in the complex plane. As an application, we prove that there are cubic Perron numbers whose Perron–Frobenius degrees are arbi...

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Bibliographic Details
Published inErgodic theory and dynamical systems Vol. 41; no. 4; pp. 1264 - 1280
Main Author YAZDI, MEHDI
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.04.2021
Subjects
Lower bounds
Original Article
11R06
37B40
entropy
37B10
Perron numbers
Perron–Frobenius degree
15B48
non-negative matrices
symbolic dynamics
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Summary:Using an idea of Doug Lind, we give a lower bound for the Perron–Frobenius degree of a Perron number that is not totally real, in terms of the layout of its Galois conjugates in the complex plane. As an application, we prove that there are cubic Perron numbers whose Perron–Frobenius degrees are arbitrary large, a result known to Lind, McMullen and Thurston. A similar result is proved for bi-Perron numbers.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2019.113