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# AFFINE MAPPINGS OF TRANSLATION SURFACES : GEOMETRY AND ARITHMETIC

@inproceedings{Gutkin2000AFFINEMO, title={AFFINE MAPPINGS OF TRANSLATION SURFACES : GEOMETRY AND ARITHMETIC}, author={Eugene Gutkin and Chris Hope Judge}, year={2000} }

- Published 2000

1. Introduction. Translation surfaces naturally arise in the study of billiards in rational polygons (see [ZKa]). To any such polygon P , there corresponds a unique translation surface, S = S(P), such that the billiard flow in P is equivalent to the geodesic flow on S (see, e.g., [Gu2], [Gu3]). There is also a classical relation between translation surfaces and quadratic differentials on a Riemann surface S. Namely, each quadratic differential induces a translation structure on a finite… CONTINUE READING

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