Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-27T05:06:27.877Z Has data issue: false hasContentIssue false
  • English
  • Français

Topological entropy of piecewise embedding maps on regular curves

Published online by Cambridge University Press:  03 July 2006

HISAO KATO
HISAO KATO
Affiliation:
Institute of Mathematics, University of Tsukuba, Ibaraki 305-8571, Japan (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

It is well known that in the dynamics of a piecewise strictly monotone (that is, piecewise embedding) map $f$ on an interval, the topological entropy can be expressed in terms of the growth of the number (that is, the lap number) of strictly monotone intervals for $f^n$. Recently, there has been an increase in the importance of fractal sets in the sciences, and many geometric and dynamical properties of fractal sets have been studied. In the present paper, we shall study topological entropy of some maps on regular curves, which are contained in the class of fractal sets. We generalize the theorem of Misiurewicz–Szlenk and Young to the cases of regular curves and dendrites.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 4 , August 2006 , pp. 1115 - 1125
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.)