48 citations · 70 across the 9 of their papers we have counts for
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Smooth projections of self-similar measures
Amir Algom, Federico Rodriguez Hertz, Zhiren Wang
We prove a Furstenberg-type criterion for a given orthogonal projection of a self-similar measure to be absolutely continuous, with quantified regularity. It requires exponential m…
Spectral gaps and Fourier decay for self-conformal measures in the plane
Amir Algom, Federico Rodriguez Hertz, Zhiren Wang
Let be a self-conformal IFS on the plane, satisfying some mild non-linearity and irreducibility conditions. We prove a uniform spectral gap estimate for the t…
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…
Logarithmic Fourier decay for self conformal measures
Amir Algom, Federico Rodriguez Hertz, Zhiren Wang
We prove that the Fourier transform of a self conformal measure on decays to at infinity at a logarithmic rate, unless the following holds: The underlying IFS is s…
Pointwise normality and Fourier decay for self-conformal measures
Amir Algom, Federico Rodriguez Hertz, Zhiren Wang
Let be a smooth IFS on , where . We provide mild conditions on the derivative cocycle that ensure that every self conformal measure is supported on p…
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…
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…
Global rigidity of higher rank Anosov algebraic actions
Federico Rodriguez Hertz, Zhiren Wang
We show that all Anosov -actions on tori and nilmanifolds without rank-one factor actions are, up to conjugacy, actions by automorphisms.