# American Institute of Mathematical Sciences

April  1999, 5(2): 291-300. doi: 10.3934/dcds.1999.5.291

## Topologically transitive homeomorphisms of quotients of tori

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

Revised  January 1998 Published  January 1999

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.
Citation: Grant Cairns, Barry Jessup, Marcel Nicolau. Topologically transitive homeomorphisms of quotients of tori. Discrete & Continuous Dynamical Systems, 1999, 5 (2) : 291-300. doi: 10.3934/dcds.1999.5.291
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