English

Lower bound for the Perron-Frobenius degrees of Perron numbers

Geometric Topology 2019-12-05 v3

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.

Keywords

Cite

@article{arxiv.1711.06885,
  title  = {Lower bound for the Perron-Frobenius degrees of Perron numbers},
  author = {Mehdi Yazdi},
  journal= {arXiv preprint arXiv:1711.06885},
  year   = {2019}
}

Comments

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