Transitivity of Euclidean-type Extensions of Hyperbolic Systems

@inproceedings{Nitica2008TransitivityOE,
  title={Transitivity of Euclidean-type Extensions of Hyperbolic Systems},
  author={Viorel Nitica and Andrei T{\"o}r{\"o}k},
  year={2008}
}
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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References

Publications referenced by this paper.
Showing 1-10 of 13 references

An open and dense set of stably ergodic diffeomorphisms in a neighborhood of a non-ergodic one

  • V. Niţică, A. Török
  • Topology 40
  • 2001

Bousch . La condition de Walters

  • I. Melbourne Field, A. Török
  • Ann . Sci . Ecole . Norm . Sup .
  • 2001

La condition de Walters

  • T. Bousch
  • Ann. Sci. Ecole. Norm. Sup. 34
  • 2001

Introduction to the modern theory of dynamical systems

  • A. Katok, B. Hasselblatt
  • Cambridge University Press
  • 1995
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