Measure rigidity beyond uniform hyperbolicity: Invariant Measures for Cartan actions on Tori

Details Measure rigidity beyond uniform hyperbolicity: Invariant Measures for Cartan actions on Tori Measure rigidity beyond uniform hyperbolicity: Invariant Measures for Cartan actions on Tori

2006-02-08

arxiv.org/abs/math/0602176v1

Mathematics

Dynamical Systems

28 pages

Scientific paper

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.

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