Hostname: page-component-cb9f654ff-w5vf4 Total loading time: 0 Render date: 2025-08-19T13:58:10.057Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic entropy, periodic orbits, and pseudo-Anosov maps

Published online by Cambridge University Press:  01 April 1998

JAROSLAW KWAPISZ  and
RICHARD SWANSON
JAROSLAW KWAPISZ
Affiliation:
Mathematics Department, SUNY at Stony Brook, NY 11794-3651, USA Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA.
RICHARD SWANSON
Affiliation:
Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717-0240, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we derive some properties of a variety of entropy that measures rotational complexity of annulus homeomorphisms, called asymptotic or rotational entropy. In previous work [KS] the authors showed that positive asymptotic entropy implies the existence of infinitely many periodic orbits corresponding to an interval of rotation numbers. In our main result, we show that a Hölder $C^1$ diffeomorphism with nonvanishing asymptotic entropy is isotopic rel a finite set to a pseudo-Anosov map. We also prove that the closure of the set of recurrent points supports positive asymptotic entropy for a ($C^0$) homeomorphism with nonzero asymptotic entropy.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 18 , Issue 2 , April 1998 , pp. 425 - 439
Copyright
1998 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.)

Article purchase

Temporarily unavailable