9 citations · 21 across the 14 of their papers we have counts for
14 papers
The symmetries of affine -systems and a program for centralizer rigidity
Danijela Damjanović, Amie Wilkinson, Chengyang Wu +1
Let Aff(X) be the group of affine diffeomorphisms of a closed homogeneous manifold X=G/B admitting a G-invariant Lebesgue-Haar probability measure . For Aff(X), let $Z^…
KAM-rigidity for parabolic affine abelian actions
Danijela Damjanovic, Bassam Fayad, Maria Saprykina
We show the following dichotomy for a linear parabolic -action on the torus with at least one step-2 generator: (i) Any affine -action with linear p…
Transitive centralizers and fibered partially hyperbolic systems
Danijela Damjanovic, Amie Wilkinson, Disheng Xu
We prove several rigidity results about the centralizer of a smooth diffeomorphism, concentrating on two families of examples: diffeomorphisms with transitive centralizer, and pert…
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…
On globally hypoelliptic abelian actions and their existence on homogeneous spaces
Danijela Damjanovic, James Tanis, Zhenqi Wang
We define globally hypoelliptic smooth actions as actions whose leafwise Laplacian along the orbit foliation is a globally hypoelliptic differential operator. When $k…
Transversal local rigidity of discrete Abelian actions on Heisenberg nilmanifolds
Danijela Damjanovic, James Tanis
In this paper we prove a perturbative result for a class of actions on Heisenberg nilmanifolds, which have Diophantine properties. Along the way we prove cohomologica…
Pathology and asymmetry: centralizer rigidity for partially hyperbolic diffeomorphisms
Danijela Damjanovic, Amie Wilkinson, Disheng Xu
We discover a rigidity phenomenon within the volume-preserving partially hyperbolic diffeomorphisms with -dimensional center. In particular, for smooth, ergodic perturbations of…
On classification of higher rank Anosov actions on compact manifold
Danijela Damjanovic, Disheng Xu
We prove global smooth classification results for TNS totally Anosov Z^k actions on general compact manifolds, under each one of the following conditions: joint integrability, reso…
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…
On conservative partially hyperbolic abelian actions with compact center foliation
Danijela Damjanovic, Disheng Xu
We consider smooth partially hyperbolic volume preserving Z^k actions on smooth manifolds, with uniformly compact center foliation. We show that under certain irreducibility condit…
Diffeomorphism group valued cocycles over higher rank abelian Anosov actions
Danijela Damjanovic, Disheng Xu
We prove that every smooth diffeomorphism group valued cocycle over certain abelian Anosov actions on tori (and more generally on infranilmanifolds), is a smooth coboundary on a fi…
Cocycle Rigidity and Splitting for some Discrete Parabolic Actions
Danijela Damjanovic, James Tanis
We prove trivialization of the first cohomology with coefficients in smooth vector fields, for a class of parabolic actions on $(SL(2, \mathbb R)\times SL(2, \mathbb…
KAM rigidity for partially hyperbolic affine Z^k actions on the torus with a rank one factor
Danijela Damjanovic, Bassam Fayad
We show that ergodic affine abelian discrete actions on the torus, that have a rank-one factor in their linear part, are locally rigid in a KAM sense if and only if the rank one fa…
Actions with globally hypoelliptic leafwise Laplacian and rigidity
Danijela Damjanovic
We prove several results concerning smooth actions with the property that their leafwise Laplacian is globally hypoelliptic. Such actions are necessarily uniquely erg…