For given positive integers dj, 1 ⩽ j⩽ ∀ s, ∑j=1sdj even, we construct a piecewise rotation map of the circle with ∑j=1sdj+s discontinuous points such that its critical iterates generate translation surfaces with singularity orders dj, 1 ⩽ j⩽ s, and with any Rauzy class associated to this singularity orders. The construction of the piecewise rotation map is combinatorial, on the other hand, the construction of the translation surfaces is based on the idea by Cruz and da Rocha.
|Title of host publication||Lecture Notes in Mathematics|
|Number of pages||39|
|Publication status||Published - 2018|
|Name||Lecture Notes in Mathematics|
ASJC Scopus subject areas
- Algebra and Number Theory