关键词: Multifractal spectrum, fractal, finite memory, spectral radius

Abstract:

The authors study recursive structures with "finite memory" in Euclidean
matric space and the multifractal decomposition of the corresponding fractals. For any two positive numbers q, β, and such a recursive structure, a linear operator V^q,β in finite dimensional space is defined. The multifractal spectrum
is given by the spectral radius of V^{q, β}.

Key words: Multifractal spectrum, fractal, finite memory, spectral radius