Outer billiards with contraction: regular polygons.

We study outer billiards with contraction outside regular polygons. For regular n-gons with n = 3, 4, 5, 6, 8, and 12, we show that as the contraction rate approaches 1, dynamics of the system converges, in a certain sense, to that of the usual outer billiardsmap. These are precisely the values of n≽3 with [Q(e2πi/n) : Q] ≼ 2. We also discuss how such convergence may fail in the case of n = 7. [ABSTRACT FROM AUTHOR]

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