5 papers
Lyapunov spectrum rigidity and simultaneous linearization for random Anosov diffeomorphisms
Aaron Brown, Yi Shi
In this paper we study the Lyapunov spectrum rigidity for random walks of expanding maps on unit circle and Anosov diffeomorphisms on -torus . Let $…
Measure rigidity for generalized u-Gibbs states and stationary measures via the factorization method
Aaron Brown, Alex Eskin, Simion Filip +1
We obtain measure rigidity results for stationary measures of random walks generated by diffeomorphisms, and for actions of on smooth manifolds. O…
Zimmer's conjecture for non-split semisimple Lie groups
Jinpeng An, Aaron Brown, Zhiyuan Zhang
We prove many new cases of Zimmer's conjecture for actions by lattices in non--split semisimple Lie groups . By prior arguments, Zimmer's conjecture reduces to study…
Boundary actions by higher-rank lattices: Classification and embedding in low dimensions, local rigidity, smooth factors
Aaron Brown, Federico Rodriguez Hertz, Zhiren Wang
We study actions by lattices in higher-rank (semi)simple Lie groups on compact manifolds. By classifying certain measures invariant under a related higher-rank abelian action (the…
Normal forms for contracting dynamics, revisited
Aaron Brown, Alex Eskin, Simion Filip +1
We revisit the theory of normal forms for non-uniformly contracting dynamics. We collect a number of lemmas and reformulations of the standard theory that will be used in other pro…