Transitivity of Heisenberg group extensions of hyperbolic systems
نویسندگان
چکیده
منابع مشابه
Stable transitivity of Heisenberg group extensions of hyperbolic systems
We consider skew-extensions with fiber the standard real Heisenberg group Hn of a uniformly hyperbolic dynamical system. We show that among the C extensions (r > 0) that avoid an obvious obstruction, those that are topologically transitive contain an open and dense set. More precisely, we show that an Hn-extension is transitive if and only if the R-extension given by the abelianization of Hn is...
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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 topological transitive. Moreover, if one considers extensions with fiber a connected nilpotent Lie group with compact commutator subgroup (for example, Hn/Z), ...
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Let f : X → X be the restriction to a hyperbolic basic set of a smooth diffeomorphism. We find several criteria for transitivity of noncompact connected Lie group extensions. As a consequence, we find transitive extensions for any finitedimensional connected Lie group extension. If, in addition, the group is perfect and has an open set of elements that generate a compact subgroup, we find open ...
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Let f : X → X be the restriction to a hyperbolic basic set of a smooth diffeomorphism. We show that in the class of C, r > 0, cocycles with fiber special Euclidean group SE(n) those that are transitive form a residual set (countable intersection of open dense sets). This result is new for n ≥ 3 odd. More generally, we consider Euclidean-type groups GnR where G is a compact connected Lie group a...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2011
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s014338571000091x