28 citations · 79 across the 13 of their papers we have counts for
15 papers
Zimmer's conjecture for non-uniform lattices: escape of mass and growth of cocycles
Aaron Brown, David Fisher, Sebastian Hurtado
We establish finiteness of low-dimensional actions of lattices in higher-rank semisimple Lie groups and establish Zimmer's conjecture for many such groups. This builds on previous…
Entropy, Lyapunov exponents, and rigidity of group actions
Aaron W. Brown, Sébastien Alvarez, Dominique Malicet +4
This text is an expanded series of lecture notes based on a 5-hour course given at the workshop entitled "Workshop for young researchers: Groups acting on manifolds" held in Teresó…
actions on manifolds by lattices in Lie groups
Aaron Brown, Danijela Damjanovic, Zhiyuan Zhang
In this paper we study Zimmer's conjecture for actions of lattice subgroup of a higher-rank simple Lie group with finite center on compact manifolds. We show that when the ra…
Zimmer's conjecture for actions of
Aaron Brown, David Fisher, Sebastian Hurtado
We prove Zimmer's conjecture for actions by finite-index subgroups of provided . The method utilizes many ingredients from our earlier proof…
Smooth ergodic theory of -actions
Aaron Brown, Federico Rodriguez Hertz, Zhiren Wang
In the first part of this paper, we formulate a general setting in which to study the ergodic theory of differentiable -actions preserving a Borel probability measure…
Invariant measures and measurable projective factors for actions of higher-rank lattices on manifolds
Aaron Brown, Federico Rodriguez Hertz, Zhiren Wang
We consider smooth actions of lattices in higher-rank semisimple Lie groups on manifolds. We define two numbers and associated with the roots system of the Lie algebr…
Smoothness of stable holonomies inside center-stable manifolds and the hypothesis in Pugh-Shub and Ledrappier-Young theory
Aaron Brown
Under a suitable bunching condition, we establish that stable holonomies inside center-stable manifolds for diffeomorphisms are uniformly bi-Lipschitz and in fact $C^{1+\…
Zimmer's conjecture: Subexponential growth, measure rigidity, and strong property (T)
Aaron Brown, David Fisher, Sebastian Hurtado
We prove several cases of Zimmer's conjecture for actions of higher-rank cocompact lattices on low dimensional manifolds. For example, if is a cocompact lattice in $\mathrm{Sl}…
Global smooth and topological rigidity of hyperbolic lattice actions
Aaron Brown, Federico Rodriguez Hertz, Zhiren Wang
In this article we prove global rigidity results for hyperbolic actions of higher-rank lattices. Suppose is a lattice in semisimple Lie group, all of whose factors have rank $2…
Continuity of Lyapunov Exponents for Cocycles with Invariant Holonomies
Lucas Backes, Aaron W. Brown, Clark Butler
We prove a conjecture of Viana which states that Lyapunov exponents vary continuously when restricted to -valued cocycles over a subshift of finite type which adm…
Measure rigidity for random dynamics on surfaces and related skew products
Aaron W. Brown, Federico Rodriguez Hertz
Given a surface and a Borel probability measure on the group of -diffeomorphisms of , we study -stationary probability measures on . We prove for hyperbolic s…
Measure rigidity for random dynamics on surfaces with positive entropy
Aaron W. Brown, Federico Rodriguez Hertz
Given a surface and a Borel probability measure on the group of -diffeomorphisms of , we study -stationary probability measures on . Assuming the positivity o…
Rigidity of measures on the torus: smooth stabilizers and entropy
Aaron W. Brown
For a nonlinear Anosov diffeomorphism of the 2-torus, we present examples of measures so that the group of -preserving diffeomorphisms is, up to zero-entropy transformations, cy…
Nonexpanding Attractors: Conjugacy to Algebraic Models and Classification in 3-Manifolds
Aaron W. Brown
We prove a result motivated by Williams's classification of expanding attractors and the Franks-Newhouse Theorem on codimension-1 Anosov diffeomorphisms: If a mixing hyperbolic att…
Constraints On Dynamics Preserving Certain Hyperbolic Sets
Aaron W. Brown
We establish two results under which the topology of a hyperbolic set constrains ambient dynamics. First if a set is a compact, transitive, expanding hyperbolic attractor of codime…