Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T04:21:40.362Z Has data issue: false hasContentIssue false
  • English
  • Français

Entropy and systoles on surfaces

Published online by Cambridge University Press:  26 July 2006

STÉPHANE SABOURAU
STÉPHANE SABOURAU
Affiliation:
Laboratoire de Mathématiques et Physique Théorique, Université de Tours, Parc de Grandmont, 37400 Tours, France (e-mail: [email protected]) and Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104-6395, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that the volume entropy of surfaces with unit systole is bounded from above by a constant which does not depend on the metric, which answers a question raised by A. Katok. This upper bound follows from a comparison between the geometric and algebraic lengths on the fundamental groups of surfaces.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 5 , October 2006 , pp. 1653 - 1669
Copyright
2006 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)