TY - JOUR
T1 - Topologically transitive homeomorphisms of quotients of tori
AU - Cairns, Grant
AU - Jessup, Barry
AU - Nicolau, Marcel
PY - 1999/4/1
Y1 - 1999/4/1
N2 - This paper considers the following question: for what finite subgroups G ⊂ GL(n, ℤ), does there exist an element A ∈ GL(n, ℤ) inducing a topologically transitive homeomorphism of double-struck T signn/G? We show that for n = 2 and 3, the only possibility is G = {±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 ≥ 4, there are relatively few irreducible examples.
AB - This paper considers the following question: for what finite subgroups G ⊂ GL(n, ℤ), does there exist an element A ∈ GL(n, ℤ) inducing a topologically transitive homeomorphism of double-struck T signn/G? We show that for n = 2 and 3, the only possibility is G = {±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 ≥ 4, there are relatively few irreducible examples.
KW - Chaos
KW - Topologically transitive
M3 - Article
SN - 1078-0947
VL - 5
SP - 291
EP - 300
JO - Discrete and Continuous Dynamical Systems
JF - Discrete and Continuous Dynamical Systems
IS - 2
ER -