Robustly transitive actions of $R^2$ on compact three manifolds

Ali Tahzibi; Carlos Maquera

Robustly transitive actions of $R^2$ on compact three manifolds

Dynamical Systems 2007-05-23 v1

Authors: Ali Tahzibi , Carlos Maquera

Abstract

In this paper, we define $C^1$ -robust transitivity for actions of $\RR^2$ on closed connected orientable manifolds. We prove that if the ambient manifold is three dimensional and the dense orbit of a robustly transitive action is not planar, then it is "degenerate" and the action is defined by an Anosov flow.

Keywords

robust transitivity actions of r^2 three manifolds anosov flows dense orbits

Cite

@article{arxiv.math/0606103,
  title  = {Robustly transitive actions of $R^2$ on compact three manifolds},
  author = {Ali Tahzibi and Carlos Maquera},
  journal= {arXiv preprint arXiv:math/0606103},
  year   = {2007}
}

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