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- W2963238466 abstract "Let $(X,mathfrak{B},unicode[STIX]{x1D707})$ be a Borel probability space. Let $T_{n}:Xrightarrow X$ be a sequence of continuous transformations on $X$ . Let $unicode[STIX]{x1D708}$ be a probability measure on $X$ such that $(1/N)sum _{n=1}^{N}(T_{n})_{ast }unicode[STIX]{x1D708}rightarrow unicode[STIX]{x1D707}$ in the weak- $ast$ topology. Under general conditions, we show that for $unicode[STIX]{x1D708}$ almost every $xin X$ , the measures $(1/N)sum _{n=1}^{N}unicode[STIX]{x1D6FF}_{T_{n}x}$ become equidistributed towards $unicode[STIX]{x1D707}$ if $N$ is restricted to a set of full upper density. We present applications of these results to translates of closed orbits of Lie groups on homogeneous spaces. As a corollary, we prove equidistribution of exponentially sparse orbits of the horocycle flow on quotients of $text{SL}(2,mathbb{R})$ , starting from every point in almost every direction." @default.
- W2963238466 created "2019-07-30" @default.
- W2963238466 creator A5071145542 @default.
- W2963238466 date "2018-07-10" @default.
- W2963238466 modified "2023-09-23" @default.
- W2963238466 title "Pointwise equidistribution and translates of measures on homogeneous spaces" @default.
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- W2963238466 doi "https://doi.org/10.1017/etds.2018.44" @default.
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