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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| Published in | Ergodic theory and dynamical systems Vol. 41; no. 4; pp. 1264 - 1280 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cambridge, UK
Cambridge University Press
01.04.2021
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| Subjects | |
| Online Access | Get full text |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | YAZDI, MEHDI |
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| DOI | 10.1017/etds.2019.113 |
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| Keywords | 11R06 37B40 entropy 37B10 Perron numbers Perron–Frobenius degree 15B48 non-negative matrices symbolic dynamics |
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| Snippet | 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... |
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| Title | Lower bound for the Perron–Frobenius degrees of Perron numbers |
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