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- W2941638371 abstract "Let $mu$ be a probability measure on $mathbb{R}/mathbb{Z}$ that is ergodic under the $times p$ map, with positive entropy. In 1995, Host showed that if $gcd(m,p)=1$ then $mu$ almost every point is normal in base $m$. In 2001, Lindenstrauss showed that the conclusion holds under the weaker assumption that $p$ does not divide any power of $m$. In 2015, Hochman and Shmerkin showed that this holds in the correct generality, i.e. if $m$ and $p$ are independent. We prove a simultaneous version of this result: for $mu$ typical $x$, if $m>p$ are independent, we show that the orbit of $(x,x)$ under $(times m, times p)$ equidistributes for the product of the Lebesgue measure with $mu$. We also show that if $m>n>1$ and $n$ is independent of $p$ as well, then the orbit of $(x,x)$ under $(times m, times n)$ equidistributes for the Lebesgue measure." @default.
- W2941638371 created "2019-05-03" @default.
- W2941638371 creator A5042472090 @default.
- W2941638371 date "2019-04-29" @default.
- W2941638371 modified "2023-09-27" @default.
- W2941638371 title "A simultaneous version of Host's equidistribution Theorem" @default.
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