The Eigenvalue Problem for Linear and Affine Iterated Function Systems
The Eigenvalue Problem for Linear and Affine Iterated Function Systems
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DOI：
10.1016/j.laa.2011.05.011
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发表时间：
2010-04
影响因子：
1.1
通讯作者：
M. Barnsley;A. Vince
中科院分区：
文献类型：
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作者：
M. Barnsley;A. Vince
线性函数L的本征值问题的中心是求解本征方程Lx=λx。本文将特征值问题从单个线性函数推广到可能由无穷多个线性或仿射函数组成的迭代函数系F。特征方程变为F（X）=λX，其中λ>0是真实的，X是紧集，F（X）= λ f∈Ff（X）.主要结果是不可约的线性迭代函数系统F有唯一的特征值λ等于F中函数的联合谱半径，相应的特征集S是中心对称的、星形的和全维的。Barabanov和Dranisnikov-Konyagin-Protasov关于联合谱半径的结果作为推论。
The eigenvalue problem for a linear function L centers on solving the eigen-equation Lx=λx. This paper generalizes the eigenvalue problem from a single linear function to an iterated function system F consisting of possibly an infinite number of linear or affine functions. The eigen-equation becomes F(X)=λX, where λ>0 is real, X is a compact set, and F(X)=⋃f∈Ff(X). The main result is that an irreducible, linear iterated function system F has a unique eigenvalue λ equal to the joint spectral radius of the functions in F and a corresponding eigenset S that is centrally symmetric, star-shaped, and full dimensional. Results of Barabanov and of Dranisnikov–Konyagin–Protasov on the joint spectral radius follow as corollaries.