Table of Contents
ISRN Geometry
Volume 2012, Article ID 165808, 15 pages
http://dx.doi.org/10.5402/2012/165808
Research Article

A Note on the Growth of Periodic Points for Commuting Toral Automorphisms

Department of Mathematics, The University of Warwick, Coventry CV4 7AL, UK

Received 1 April 2012; Accepted 3 May 2012

Academic Editors: J. Keesling and S. Troubetzkoy

Copyright © 2012 Mark Pollicott. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. Miles and T. Ward, “Uniform periodic point growth in entropy rank one,” Proceedings of the American Mathematical Society, vol. 136, no. 1, pp. 359–365, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. D. Damjanović and A. Katok, “Local rigidity of partially hyperbolic actions I. KAM method and k actions on the torus,” Annals of Mathematics. Second Series, vol. 172, no. 3, pp. 1805–1858, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. S. Waddington, “The prime orbit theorem for quasihyperbolic toral automorphisms,” Monatshefte für Mathematik, vol. 112, no. 3, pp. 235–248, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. A. Katok, S. Katok, and K. Schmidt, “Rigidity of measurable structure for d-actions by automorphisms of a torus,” Commentarii Mathematici Helvetici, vol. 77, no. 4, pp. 718–745, 2002. View at Publisher · View at Google Scholar
  5. L. Krönecker, “Zwei sätse über Gleichungen mit ganzzahligen Coefcienten,” Journal für die reine und angewandte Mathematik, vol. 53, pp. 173–175, 1857. View at Google Scholar
  6. C. Smyth, “The Mahler measure of algebraic numbers: a survey,” in Number Theory and Polynomials, vol. 352 of London Mathematical Society Lecture Note Series, pp. 322–349, Cambridge University Press, Cambridge, UK, 2008. View at Publisher · View at Google Scholar
  7. A. Manning, “There are no new Anosov diffeomorphisms on tori,” American Journal of Mathematics, vol. 96, pp. 422–429, 1974. View at Publisher · View at Google Scholar · View at Zentralblatt MATH