Abstract
We consider groups generated by real analytic diffeomorphisms of a compact manifold close to the identity. We show that the dynamics of such a group is recurrent unless the group satisfies a very particular property, similar to solvability. We study in detail the case of diffeomorphisms of the circle and the disc.
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Ghys, E. Sur les groupes engendrés par des difféomorphismes proches de l'identité. Bol. Soc. Bras. Mat 24, 137–178 (1993). https://doi.org/10.1007/BF01237675
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DOI: https://doi.org/10.1007/BF01237675