Windows in one-dimensional maps

The window structure in the chaotic part of the parameter space of one-dimensional maps is described in detail. Explicit expressions are derived for both the internal structure and the width of the periodic windows, by considering a universal local submap. Both features are found to depend only on the order of the extremum of this submap. Moreover, the windows can be ordered in trees. The various branches of these trees define (accumulating) families of windows, for which exact scaling relations can be derived. Finally, we discuss an extension of our description of window phenomena into two dimensions.

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