Abstract
AbstractWe show that amongCrextensions (r>0) of a uniformly hyperbolic dynamical system with fiber the standard real Heisenberg group ℋnof 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.
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