Abstract
Piecewise linear maps are often used to approximate continuous mappings. In this paper the evolution of periodic solutions, bifurcation patterns, and chaotic motions of piecewise linear maps is studied in detail. Our particular interest is in discovering special features of these mappings. The conventional bifurcation pattern changes drastically: for instance, a pitchfork bifurcation is replaced by a square-shape pitchfork one. Most features are best appreciated through one-dimensional maps which are exclusively studied in this paper
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