Abstract
Basic geometrical and topological features aredescribed for discontinuous systems modelling power converters. Theglobal Poincaré mapconsidered arisesnaturallyfrom the samplingprocess in the oscillatory forced system. It is shown that this mapbelongs to the class of two-dimensional invertible continuous but onlypiecewise-smooth maps. It also contains a singular point at which criticalcurves accumulate. A method is found to computeanalytically thecharacteristic multipliers of a periodic orbit, giving a powerful tool toobtain the values for smooth and non-smooth bifurcations. The images ofthe regions of multiple crossings are studiedgeometrically and thennumerical computation allows oneto deduce the existence of a Smale horseshoemechanism in the map and also to obtain chaotic motion. Finally, theexistence of a chaotic attractor is justified with the addition of5T-recurrent behaviour near a singular point.
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