Lower bound for the Perron-Frobenius degrees of Perron numbers

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. 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 biPerron numbers.

To appear in Ergodic Theory and Dynamical Systems, 15 pages, 4 figures

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