a1 Department of Mathematics, University of Surrey, Guildford, Surrey GU2 7XH, UK (email: email@example.com)
a2 Department of Mathematics, West Chester University, West Chester, PA 19383, USA (email: firstname.lastname@example.org)
a3 Institute of Mathematics of the Romanian Academy, PO Box 1–764, RO-70700 Bucharest, Romania
a4 Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA (email: email@example.com)
We show that among Cr extensions (r>0) of a uniformly hyperbolic dynamical system with fiber the standard real Heisenberg group ℋn of dimension 2n+1, those that avoid an obvious obstruction to topological transitivity are generically topologically transitive. Moreover, if one considers extensions with fiber a connected nilpotent Lie group with a compact commutator subgroup (for example ℋn/ℤ), among those that avoid the obvious obstruction, topological transitivity is open and dense.
(Received May 14 2010)
(Revised November 16 2010)
(Online publication April 05 2011)