Hostname: page-component-77c89778f8-n9wrp Total loading time: 0 Render date: 2024-07-24T02:23:24.086Z Has data issue: false hasContentIssue false
  • English
  • Français

Homeomorphisms without the pseudo-orbit tracing property

Published online by Cambridge University Press:  22 January 2016

Nobuo Aoki
Nobuo Aoki*
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Fukazawa, Setagaya-ku, Tokyo 158, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Recently, A. Morimoto [5] proved that every isometry of a compact Riemannian manifold of positive dimension has not the pseudo-orbit tracing property, and that if a homeomorphism of a compact metric space has the pseudo-orbit tracing property then Eφ— 0φ(see § 1 for definition). The purpose of this paper is to show that every distal homeomorphism of a compact connected metric space has not the pseudo-orbit tracing property.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 88 , December 1982 , pp. 155 - 160
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

References

[ 1 ] Aoki, N., The splitting of zero-dimensional automorphisms and its application, (to appear in Collq. Math.)Google Scholar
[ 2 ] Ellis, R., Lectures on Topological Dynamics, Benjamin, New York 1969.Google Scholar
[ 3 ] Bowen, R., ω-limit sets for Axiom A diffeomorphisms, J. Diff. Eq., 18 (1975), 333–339.Google Scholar
[ 4 ] Kuratowskii, C., Topologie, Vol. II, Warzawa, 1961.Google Scholar
[ 5 ] Morimoto, A., Stochastically stable diffeomorphisms and Takens conjecture, (preprint)Google Scholar
[ 6 ] Morimoto, A., Stochastic stability of group automorphisms, (preprint)Google Scholar
[ 7 ] Walters, P., Ergodic Theory-Introductory Lectures, Springer Lee. notes, No. 458, 1975.Google Scholar