论文标题
抛物线地毯
Parabolic carpets
论文作者
论文摘要
我们介绍并研究了一个非统一和不均匀收缩的迭代功能系统的家族。我们指的是抛物线地毯等系统的吸引者。粗略地说，它们可能被认为是允许具有抛物线固定点的自动地毯的非线性类似物。我们计算了抛物线地毯上支持的一类弱吉布斯措施以及地毯本身的盒子尺寸的$ l^q $ -spectrum。
We introduce and study a family of non-conformal and non-uniformly contracting iterated function systems. We refer to the attractors of such systems as parabolic carpets. Roughly speaking they may be thought of as nonlinear analogues of self-affine carpets which are allowed to have parabolic fixed points. We compute the $L^q$-spectrum of a class of weak Gibbs measures supported on parabolic carpets as well as the box dimensions of the carpet itself.
