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We also report an example of a period tripling cascade that arises from this system.","abstract_html":"We investigate the iterative dynamics of symplectic piecewise-affine elliptic rotation maps associated with matrices with non-integer entries, 0-11a , where -2 &lt; a &lt; 2. We explain how their singularity and periodicity structures develop in general. In a special case, a = +/- 2 , we completely determine the orbit structure and the singularity structure, and answer conjectures by Tresser, Adler and Kitchens. 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We explain how their singularity and periodicity structures develop in general. In a special case, a = +/- 2 , we completely determine the orbit structure and the singularity structure, and answer conjectures by Tresser, Adler and Kitchens. We also report an example of a period tripling cascade that arises from this system.","Made available in DSpace on 2015-09-28T15:20:34Z (GMT). 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We explain how their singularity and periodicity structures develop in general. In a special case, a = +/- 2 , we completely determine the orbit structure and the singularity structure, and answer conjectures by Tresser, Adler and Kitchens. We also report an example of a period tripling cascade that arises from this system.","Made available in DSpace on 2015-09-28T15:20:34Z (GMT). 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