10 citations · 28 across the 23 of their papers we have counts for
18 papers · 1 filter
On the work of Zhiren Wang on rigidity in dynamics
Ralf Spatzier
In honor of Zhiren Wang on the occasion of being awarded the Brin Prize, we report on his exciting and deep work on rigidity of higher rank abelian groups and lattices in higher ra…
Boundary actions of lattices and local semi-rigidity
Chris Connell, Mitul Islam, Thang Nguyen +1
We consider actions of cocompact lattices in semisimple Lie groups of the noncompact type on their boundaries , a parabolic group, the so-called standard actions. We show…
The Zimmer Program for partially hyperbolic actions
Danijela Damjanovic, Ralf Spatzier, Kurt Vinhage +1
Zimmer's superrigidity theorems on higher rank Lie groups and their lattices launched a program of study aiming to classify actions of semisimple Lie groups and their lattices, kno…
Exponential mixing, KAM and smooth local rigidity
Ralf Spatzier, Lei Yang
Consider actions of by ergodic automorphisms on a compact nilmanifolds for . We show that small perturbations of such higher rank partially hyperbolic actio…
Carnot metrics, Dynamics and Local Rigidity
Chris Connell, Thang Nguyen, Ralf Spatzier
This paper develops new techniques for studying smooth dynamical systems in the presence of a \CC metric. Principally, we employ the theory of Margulis-Mostow, Métivier, Mitchell a…
Cartan Actions of Higher Rank Abelian Groups and their Classification
Ralf Spatzier, Kurt Vinhage
We study actions on arbitrary compact manifolds with a projectively dense set of Anosov elements and 1-dimensional coarse Lyapunov foliations.…
Smooth Factors of Projective Actions of Higher Rank Lattices and Rigidity
Alexander Gorodnik, Ralf Spatzier
We study smooth factors of the standard actions of lattices in higher rank semisimple Lie groups on flag manifolds. Under a mild condition on existence of a single differentiable s…
Exponential Mixing and Smooth Classification of Commuting Expanding Maps
Ralf Spatzier, Lei Yang
We show that genuinely higher rank expanding actions of abelian semi-groups on compact manifolds are -conjugate to affine actions on infra-nilmanifolds. This is based o…
On the work of Rodriguez Hertz on rigidity in dynamics
Ralf Spatzier
This paper is a survey about recent progress in measure rigidity and global rigidity of Anosov actions, and celebrates the profound contributions by Federico Rodriguez Hertz to rig…
Equilibrium measures for certain isometric extensions of Anosov systems
Ralf Spatzier, Daniel Visscher
We prove that for the frame flow on a negatively curved, closed manifold of odd dimension other than 7, and a Holder continuous potential that is constant on fibers, there is a uni…
Mixing Properties of Commuting Nilmanifold Automorphisms
Alexander Gorodnik, Ralf Spatzier
We study mixing properties of commutative groups of automorphisms acting on compact nilmanifolds. Assuming that every nontrivial element acts ergodically, we prove that such action…
Exponential Mixing of Nilmanifold Automorphisms
Alexander Gorodnik, Ralf Spatzier
We study dynamical properties of automorphisms of compact nilmanifolds and prove that every ergodic automorphism is exponentially mixing and exponentially mixing of higher orders.…
Global Rigidity of Higher Rank Anosov Actions on Tori and Nilmanifolds
David Fisher, Boris Kalinin, Ralf Spatzier +1
We show that sufficiently irreducible Anosov actions of higher rank abelian groups on tori and nilmanifolds are smoothly conjugate to affine actions.
Totally non-symplectic Anosov actions on tori and nilmanifolds
David Fisher, Boris Kalinin, Ralf Spatzier
We show that sufficiently irreducible totally non-symplectic Anosov actions of higher rank abelian groups on tori and nilmanifolds are smoothly conjugate to affine actions.
Regularity of conjugacies of algebraic actions of Zariski dense groups
Alexander Gorodnik, Theron Hitchman, Ralf Spatzier
Let α_0 be an affine action of a discrete group Γon a compact homogeneous space X and α_1 a smooth action of Γon X which is C^1-close to α_0. We show that under some conditions, ev…
On the Classification of Cartan Actions
Boris Kalinin, Ralf Spatzier
We study higher rank Cartan actions on compact manifolds preserving an ergodic measure with full support. In particular, we classify actions by with whose one-pa…
Rigidity of the measurable structure for algebraic actions of higher rank abelian groups
Boris Kalinin, Ralf Spatzier
We investigate rigidity of measurable structure for higher rank abelian algebraic actions. In particular, we show that ergodic measures for these actions fiber over a 0 entropy mea…
New examples of manifolds with completely integrable geodesic flows
Gabriel Paternain, Ralf J. Spatzier
We construct Riemannian manifolds with completely integrable geodesic flows, in particular various nonhomogeneous examples. The methods employed are a modification of Thimm's metho…