The Hopf–Tsuji–Sullivan dichotomy in higher rank and applications to Anosov subgroups

Marc Burger, Or Landesberg, Minju Lee, Hee Oh

Type: Article

Publication Date: 2023-01-01

Citations: 10

DOI: https://doi.org/10.3934/jmd.2023008

Abstract

We establish an extension of the Hopf–Tsuji–Sullivan dichotomy to any Zariski dense discrete subgroup of a semisimple real algebraic group $ G $. We then apply this dichotomy to Anosov subgroups of $ G $, which surprisingly presents a different phenomenon depending on the rank of the ambient group $ G $.

Locations

arXiv (Cornell University) - View - PDF
Journal of Modern Dynamics - View - PDF

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