Dimension gap and variational principle for Anosov representations

François Ledrappier; Pablo Lessa

Dimension gap and variational principle for Anosov representations

Dynamical Systems 2023-12-22 v3

Authors: François Ledrappier , Pablo Lessa

Abstract

We consider a representation of a finitely generated CAT(--K) group $\Gamma$ in SL(d, R) that is Zariski dense and k-Anosov for at least two values of k. We exhibit a gap for the Minkowski dimension of minimal sets for the action of $\Gamma$ on flags spaces. The proof uses a variational principle for the action on partial flags.

Cite

@article{arxiv.2310.13465,
  title  = {Dimension gap and variational principle for Anosov representations},
  author = {François Ledrappier and Pablo Lessa},
  journal= {arXiv preprint arXiv:2310.13465},
  year   = {2023}
}

Comments

This paper replaces ''Dimension gap for the limit sets of Anosov representations''. The use of Connel-Muchnik 07 in the proof of the variational principle was erroneous. In this new version, we directly prove the variational principle Theorem 1.7

Dimension gap and variational principle for Anosov representations

Abstract

Cite

Comments

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