TY - JOUR

T1 - Parabolic Perturbations of Unipotent Flows on Compact Quotients of SL (3 , R)

AU - Ravotti, Davide

PY - 2019

Y1 - 2019

N2 - We consider a family of smooth perturbations of unipotent flows on compact quotients of SL(3 , R) which are not time-changes. More precisely, given a unipotent vector field, we perturb it by adding a non-constant component in a commuting direction. We prove that, if the resulting flow preserves a measure equivalent to Haar, then it is parabolic and mixing. The proof is based on a geometric shearing mechanism together with a non-homogeneous version of Mautner Phenomenon for homogeneous flows. Moreover, we characterize smoothly trivial perturbations and we relate the existence of non-trivial perturbations to the failure of cocycle rigidity of parabolic actions in SL(3 , R).

AB - We consider a family of smooth perturbations of unipotent flows on compact quotients of SL(3 , R) which are not time-changes. More precisely, given a unipotent vector field, we perturb it by adding a non-constant component in a commuting direction. We prove that, if the resulting flow preserves a measure equivalent to Haar, then it is parabolic and mixing. The proof is based on a geometric shearing mechanism together with a non-homogeneous version of Mautner Phenomenon for homogeneous flows. Moreover, we characterize smoothly trivial perturbations and we relate the existence of non-trivial perturbations to the failure of cocycle rigidity of parabolic actions in SL(3 , R).

UR - http://www.scopus.com/inward/record.url?scp=85061027607&partnerID=8YFLogxK

U2 - 10.1007/s00220-019-03348-0

DO - 10.1007/s00220-019-03348-0

M3 - Article

AN - SCOPUS:85061027607

VL - 371

SP - 331

EP - 351

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -