Sliding Singularities of Bounded Invertible Planar Piecewise Isometric Dynamics
نویسندگان
چکیده
It is known that the singularities of bounded invertible piecewise isometric dynamical systems in Euclidean plane can be classified as, removable, sliding and shuffling singularities, based upon their geometrical aspects. Moreover, it is known that the Devaney-chaos of the bounded invertible piecewise isometric systems can be generated only from the sliding singularities, while the other singularities remain innocuous. For this reason, we concentrate our efforts on the investigation of the sliding singularity. We begin with re-establishing the distinction between the sliding and shuffling singularities in simpler terms. And then, we calculate the sliding ratios explicitly for a class of invertible planar piecewise isometric systems. Keywords— Devaney-chaos, Piecewise continuous dynamical system, Piecewise isometric dynamical system, Singularity.
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