TY - CHAP

T1 - A Piecewise rotation of the circle, IPR maps and their connection with translation surfaces

AU - Inoue, Kae

AU - Nakada, Hitoshi

N1 - Funding Information:
Acknowledgements The second author was partially supported by JSPS grants No. 16K13766 and JSPS Core-to-core program, “Foundation of a Global Research Cooperative Center in Mathematics focused on Number Theory and Geometry”.
Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-319-74908-2_19

DO - 10.1007/978-3-319-74908-2_19

M3 - Chapter

AN - SCOPUS:85048679266

T3 - Lecture Notes in Mathematics

SP - 393

EP - 431

BT - Lecture Notes in Mathematics

PB - Springer Verlag

ER -