角乘映射的悬浮半流中相关性的衰减
Decay of correlations in suspension semi-flows of angle-multiplying maps
摘要：
考虑圆上角乘映射的悬置半流。在天花板函数的$C^r$一般条件下，我们证明了存在包含在$L^2$空间中的各向异性索伯列夫空间，使得时间- $t$ -映射的Perron-Frobenius算子作用于该空间，并且该作用的本质谱半径以最小扩张率的倒数的平方根为界.这导致了对关联衰减的精确描述，推广了M.波利科特
英文摘要：
We consider suspension semi-flows of angle-multiplying maps on the circle. Under a $C^r$generic condition on the ceiling function, we show that there exists an anisotropic Sobolev space contained in the $L^2$ space such that the Perron-Frobenius operator for the time-$t$-map acts on it and that the essential spectral radius of that action is bounded by the square root of the inverse of the minimum expansion rate. This leads to a precise description on decay of correlations and extends the result of M. Pollicott.
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