Linear expansions, strictly ergodic homogeneous cocycles and fractals
Linear expansions, strictly ergodic homogeneous cocycles and fractals
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线性展开、严格遍历齐次余循环和分形
DOI：
10.1007/bf02773474
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发表时间：
1998
影响因子：
1
通讯作者：
T. Kamae
中科院分区：
文献类型：
--
作者：
T. Kamae
我们考虑一个紧致空间Θ，它的加法运算和R+乘法运算满足分配定律。此外，R-动作是严格遍历的。这种Θ被构造为对应于加权替换的有色瓷砖空间，这是分段线性的f-展开式的一种自然推广。我们定义了一个齐次Θ上的余圈，它在文[2]中被称为具有标度性质的余圈。这是允许连续标度的分形函数的一种实现。这也定义了一个具有严格遍历的平稳增量的自相似过程，该过程的熵为0。
We consider a compact space Θ on whichRacts additively andR+acts multiplicatively satisfying the distributive law. Moreover,R-action is strictly ergodic. Such Θ is constructed as a space of colored tilings corresponding to a weighted substitution, which is a kind of natural extension of thef-expansion for a piecewise linearf. We define a homogeneous cocycleFon Θ, which was called a cocycle with the scaling property in [2]. This is a realization of fractal functions which admit the continuous scalings. This also defines a self-similar process with strictly ergodic, stationary increments which has 0 entropy.