Measure rigidity beyond uniform hyperbolicity: Invariant Measures for Cartan actions on Tori
Dynamical Systems
2007-05-23 v1
Abstract
We prove that every smooth action of Z^k, k>1, on the (k+1)-dimensional torus homotopic to an action by hyperbolic linear maps preserves an absolutely continuous measure. This is a first known result concerning abelian groups of diffeomorphisms where existence of an invariant geometric structure is obtained from homotopy data.
Cite
@article{arxiv.math/0602176,
title = {Measure rigidity beyond uniform hyperbolicity: Invariant Measures for Cartan actions on Tori},
author = {Boris Kalinin and Anatole Katok},
journal= {arXiv preprint arXiv:math/0602176},
year = {2007}
}
Comments
28 pages