Unstable Orbits and Milnor Attractors in the Discontinuous Flat Top Tent Map

In this work we consider the discontinuous flat top tent map which represents an example for discontinuous piecewise-smooth maps, whereby the system function is constant on some interval. Such maps show several characteristics caused by this constant value which are still insufficiently investigated. In this work we demonstrate that in the discontinuous flat top tent map every unstable periodic orbit may become a Milnor attractor. Moreover, it turns out that there exists a strong connection between stable and unstable orbits and that the appearance of a single unstable orbit may cause an infinite number of stable orbits to appear. Based on this connection we provide a more precise explanation of the recently discovered self-similar bifurcation scenario occurring in the discontinuous flat top tent map denoted as the nested period incrementing scenario.