Simple Maps with Fractal Diffusion Coefficients

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Abstract
We consider chains of one-dimensional, piecewise linear, chaotic maps with uniform slope. We study the diffusive behavior of an initially nonuniform distribution of points as a function of the slope of the map by solving the Frobenius-Perron equation. For Markov partition values of the slope, we relate the diffusion coefficient to eigenvalues of the topological transition matrix. The diffusion coefficient obtained shows a fractal structure as a function of the slope of the map. This result may be typical for a wide class of maps, such as two-dimensional sawtooth maps.