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Transitivity of Heisenberg group extensions of hyperbolic systems

Published online by Cambridge University Press:  05 April 2011

IAN MELBOURNE ,
VIOREL NIŢICĂ  and
ANDREI TÖRÖK
IAN MELBOURNE
Affiliation:
Department of Mathematics, University of Surrey, Guildford, Surrey GU2 7XH, UK (email: [email protected])
VIOREL NIŢICĂ
Affiliation:
Department of Mathematics, West Chester University, West Chester, PA 19383, USA (email: [email protected]) Institute of Mathematics of the Romanian Academy, PO Box 1–764, RO-70700 Bucharest, Romania
ANDREI TÖRÖK
Affiliation:
Institute of Mathematics of the Romanian Academy, PO Box 1–764, RO-70700 Bucharest, Romania Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA (email: [email protected])
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Abstract

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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 1 , February 2012 , pp. 223 - 235
Copyright
Copyright © Cambridge University Press 2011

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