Abstract:
We describe an attracting piecewise rotation with two atoms with a self-similar structure of periodic domains on its attractor which resembles Sierpi'nski's gasket. Besides its natural beauty, this example appears a return map in certain piecewise affine maps on the torus which have been studied by Adler, Kitchens, and Tresser, and by a number of other researchers advancing the theory of digital filters. 1
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