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Veech groups, irrational billiards and stable abelian differentials

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  • We describe Veech groups of flat surfaces arising from irrational angled polygonal billiards or irreducible stable abelian differentials. For irrational polygonal billiards, we prove that these groups are non-discrete subgroups of $\rm SO(2,\mathbf{R})$ and we calculate their rank.
    Mathematics Subject Classification: Primary: 37D50; Secondary: 37J35.


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