论文标题
$ l^q $ - 平面非统一吸引子的措施
$L^q$-spectra of measures on planar non-conformal attractors
论文作者
论文摘要
我们研究了某些非线性地图生成的飞机中的$ l^q $ - 镜头。特别是我们考虑了由$ c^{1+α} $组成的迭代功能系统的吸引子，并且在每个点上，雅各布是一个下部的三角形矩阵，但在条目上均具有自然的统治条件。我们通过使用适当定义的奇异值函数和适当的压力函数来计算在此类集合上支持的Bernoulli度量的$ L^Q $ -Spectrum。
We study the $L^q$-spectrum of measures in the plane generated by certain nonlinear maps. In particular we consider attractors of iterated function systems consisting of maps whose components are $C^{1+α}$ and for which the Jacobian is a lower triangular matrix at every point subject to a natural domination condition on the entries. We calculate the $L^q$-spectrum of Bernoulli measures supported on such sets by using an appropriately defined analogue of the singular value function and an appropriate pressure function.
