| Abstract: |
| The notion of the critical iterate of piecewise rotation maps of the circle was first introduced by Cruz and da Rocha (2005). We will see that for any given singularity order vector and any marked singularity, there exists a piecewise rotation of the circle such that one of discontinuous points and one of its associated critical iterate generate a translation surface which has the given singularity orders with the given marked singularity. |
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