Abstract
In this paper, the dynamics of skew tent maps are classified in terms of two bifurcation parameters. In time series analysis such maps are usually referred to as continuous threshold autoregressive models (TAR(1)-models) after Tong (Non-Linear Time Series, Clarendon Press, Oxford, UK, 1990). This study contains results simplifying the use of TAR(1)-models considerably, e.g. if a periodic attractor exists it is unique. On the other hand, we also claim that care must be exercised when TAR models are used. In fact, they possess a very special type of dynamical pattern with respect to the bifurcation parameters and their transition to chaos is far from standard.
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