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arXiv · 1303.7074

Invariant Distributions for homogeneous flows

Livio Flaminio·Giovanni Forni·Federico Rodriguez Hertz
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Abstract

We prove that every homogeneous flow on a finite-volume homogeneous manifold has countably many independent invariant distributions unless it is conjugate to a linear flow on a torus. We also prove that the same conclusion holds for every affine transformation of a homogenous space which is not conjugate to a toral translation. As a part of the proof, we have that any smooth partially hyperbolic flow on any compact manifold has countably many distinct minimal sets, hence countably many distinct ergodic probability measures. As a consequence, the Katok and Greenfield-Wallach conjectures hold in all of the above cases.

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Livio Flaminio, Giovanni Forni, Federico Rodriguez Hertz. 2013-03-28. Invariant Distributions for homogeneous flows. https://arxiv.org/abs/1303.7074

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