Abstract
An efficient method to determine the measure of fat-fractal sets of parameter values giving rise to chaos in a wide class of nonlinear mappings on finite intervals is introduced. The method is based on perturbing a given map by a piecewise linear term -mchemically bondxchemically bond with mgreater than or equal to0. For nonzero values of the perturbation strength m the maps under study are chaotic on intervals in the nonlinearity parameter. As m diminishes, the number of these intervals increases, whereas their average length decreases. Accordingly, the measure of the studied fat fractals is defined as a limit (for m..-->..0 of the product of the number of chaotic intervals and their average size.
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