论文标题
对角线内态对2道龙的共同不变措施的作用
Actions of diagonal endomorphisms on conformally invariant measures on the 2-torus
论文作者
论文摘要
令$ν$为一种概率度量，在内态$（\ times p，\ times p）$下是e godic，torus $ \ mathbb {t}^2 $，因此对于某些非principal投射$π$。我们表明，如果两个$ m \ neq n $均独立于$ p $，则$ n $ n $典型点的$（\ times m，\ times n）$ orbits将对Lebesgue度量等级。如果$ m> p $，则通常是$（\ times m，\ times p）$ orbits在$ y $ - 轴上的边际$μ$的lebesgue Measure的产品。对于某些自我相似的度量$ν$，我们还以同样的精神证明结果。这些是应得的结果的较高维度类似物（除其他），lindenstrauss和Hochman-Shmerky。
Let $ν$ be a probability measure that is ergodic under the endomorphism $(\times p, \times p)$ of the torus $\mathbb{T}^2$, such that $\dim πμ< \dim μ$ for some non-principal projection $π$. We show that, if both $m\neq n$ are independent of $p$, the $(\times m, \times n)$ orbits of $ν$ typical points will equidistribute towards the Lebesgue measure. If $m>p$ then typically the $(\times m, \times p)$ orbits will equidistribute towards the product of the Lebesgue measure with the marginal of $μ$ on the $y$-axis. We also prove results in the same spirit for certain self similar measures $ν$. These are higher dimensional analogues of results due (among others) to Host, Lindenstrauss, and Hochman-Shmerkin.
