The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent map and its application as a border collision normal form are discussed. We describe the period adding and incrementing bifurcation structures in the domain of regular dynamics of a discontinuous piecewise-linear map, and the related bandcount adding and incrementing structures in the domain of robust chaos. Also, we explain how these structures originate from particular codimension-two bifurcation points which act as organizing centers. In addition, we present the map replacement technique which provides a powerful tool for the description of bifurcation structures in piecewise-linear and other form of invariant maps to a much further extent than the other approaches.

Das 19. Fachgespr ch Autonome Mobile Systeme (AMS 2005) ist ein Forum, das Wissenschaftlerinnen und Wissenschaftlern aus Forschung und Industrie, die auf dem Gebiet der autonomen mobilen Systeme arbeiten, eine Basis f r den Gedakenaustausch bietet und wissenschfltiche Diskussionen sowie Kooperationen auf diesem Forschungsgebiet f rdert bzw. initiiert. Ausgew hlte Beitr ge zu den Themen Kooperative Systeme, Bildverarbeitung, Lokalisierung und Kartographierung, Outdoor-Systeme, Fahrerassistenzsysteme, Kognitive Sensordatenverarbeitung, Architekturen und Anwendungen sowie Steuerung und Navigation bilden den Inhalt dieses Bandes.