Topologically transitive homeomorphisms of quotients of tori

Grant Cairns; Barry Jessup; Marcel Nicolau

doi:10.3934/dcds.1999.5.291

Article Contents

1999, Volume 5, Issue 2: 291-300. Doi: 10.3934/dcds.1999.5.291

This issue Previous Article Optimal control of systems governed by some elliptic equations Next Article Multiple solutions of Neumann elliptic problems with critical nonlinearity

Topologically transitive homeomorphisms of quotients of tori

1.
School of Mathematics, La Trobe University, Melbourne, Australia 3083
2.
Department of Mathematics, University of Ottawa, Ottawa, Canada K1N6N5
3.
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra

Revised: January 1998

Published: April 1999

Abstract Related Papers Cited by

Abstract

This paper considers the following question: for what finite subgroups $G\subset GL(n, \mathbb Z)$, does there exist an element $A\in GL(n, \mathbb Z)$ inducing a topologically transitive homeomorphism of $T^n$/$G$ We show that for $n = 2$ and 3, the only possibility is $G =\{\pm I\}$. Curiously, in higher dimension the structure is less restrictive. We give a variety of examples in dimension 4. Nevertheless, we show that in dimension $\geq 4$, there are relatively few irreducible examples.

Keywords:

Topologically transitive,
chaos.

Mathematics Subject Classification: 54H20, 57S25.

Citation:

Article Metrics

HTML views() PDF downloads(106) Cited by(0)

Topologically transitive homeomorphisms of quotients of tori

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Topologically transitive homeomorphisms of quotients of tori

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content