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arXiv · 2010.04547

Locally unipotent invariant measures and limit distribution of a sequence of polynomial trajectories on homogeneous spaces

Han Zhang
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Abstract

Let $G$ be a Lie group and $\Gamma$ be a lattice in $G$. We introduce the notion of locally unipotent invariant measures on $G/\Gamma$. We then prove that under some conditions, the limit measure supported on the image of polynomial trajectories on $G/\Gamma$ is locally unipotent invariant, thus give a partial answer to an equidistribution problem for higher dimensional polynomial trajectories on homogeneous spaces, which was raised by Shah in \cite{shah1994limit}. The proof relies on Ratner's measure classification theorem, linearization technique for polynomial trajectories near singular sets and a twisting technique of Shah.

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Han Zhang. 2020-10-09. Locally unipotent invariant measures and limit distribution of a sequence of polynomial trajectories on homogeneous spaces. https://arxiv.org/abs/2010.04547

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