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On classification of higher rank Anosov actions on compact manifold

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Abstract

We prove global smooth classification results for Anosov ℤk actions on general compact manifolds, under certain irreduciblity conditions and the presence of sufficiently many Anosov elements. In particular, we remove all the uniform control assumptions which were used in all the previous results towards the Katok-Spatzier global rigidity conjecture on general manifolds. The main idea is to create a new mechanism labelled nonuniform redefining argument, to prove continuity of certain dynamically-defined objects. This leads to uniform control for higher-rank actions and should apply to more general rigidity problems in dynamical systems.

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Authors and Affiliations

  1. Department of Mathematics, Kungliga Tekniska Högskolan, Lindstedtsvägen 25, SE-100 44, Stockholm, Sweden

    Danijela Damjanović

  2. Department of Mathematics, The University of Chicago, Chicago, IL, 60637, US

    Disheng Xu

Authors
  1. Danijela Damjanović
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  2. Disheng Xu
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Correspondence to Disheng Xu.

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Dedicated to the memory of Anatole Katok

The first author is supported by the Swedish Research Council grant 2015-04644.

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Damjanović, D., Xu, D. On classification of higher rank Anosov actions on compact manifold. Isr. J. Math. 238, 745–806 (2020). https://doi.org/10.1007/s11856-020-2038-4

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  • DOI: https://doi.org/10.1007/s11856-020-2038-4

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