Transitivity of Euclidean-type Extensions of Hyperbolic Systems

  title={Transitivity of Euclidean-type Extensions of Hyperbolic Systems},
  author={Viorel Nitica and Andrei T{\"o}r{\"o}k},
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 acting linearly on R. When FixG = {0}, it is again the case that the transitive cocycles are residual… CONTINUE READING

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