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• W3103240730 abstract "We study a parametric family of piecewise rotations of the torus, in the limit in which the rotation number approaches the rational value 1/4. There is a region of positive measure where the discontinuity set becomes dense in the limit; we prove that in this region the area occupied by stable periodic orbits remains positive. The main device is the construction of an induced map on a domain with vanishing measure; this map is the product of two involutions, and each involution preserves all its atoms. Dynamically, the composition of these involutions represents linking together two sector maps; this dynamical system features an orderly array of stable periodic orbits having a smooth parameter dependence, plus irregular contributions which become negligible in the limit." @default.
• W3103240730 created "2020-11-23" @default.
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• W3103240730 date "2010-08-26" @default.
• W3103240730 modified "2023-10-16" @default.
• W3103240730 title "Approach to a rational rotation number in a piecewise isometric system" @default.
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• W3103240730 doi "https://doi.org/10.1088/0951-7715/23/10/017" @default.
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