### Abstract

For given positive integers d_{j}, 1 ⩽ j⩽ ∀ s, ∑j=1sdj even, we construct a piecewise rotation map of the circle with ∑_{j=1} ^{s}dj+s discontinuous points such that its critical iterates generate translation surfaces with singularity orders d_{j}, 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.

Original language | English |
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Title of host publication | Lecture Notes in Mathematics |

Publisher | Springer Verlag |

Pages | 393-431 |

Number of pages | 39 |

DOIs | |

Publication status | Published - 2018 Jan 1 |

### Publication series

Name | Lecture Notes in Mathematics |
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Volume | 2213 |

ISSN (Print) | 0075-8434 |

### Fingerprint

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Lecture Notes in Mathematics*(pp. 393-431). (Lecture Notes in Mathematics; Vol. 2213). Springer Verlag. https://doi.org/10.1007/978-3-319-74908-2_19

**A Piecewise rotation of the circle, IPR maps and their connection with translation surfaces.** / Inoue, Kae; Nakada, Hitoshi.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Lecture Notes in Mathematics.*Lecture Notes in Mathematics, vol. 2213, Springer Verlag, pp. 393-431. https://doi.org/10.1007/978-3-319-74908-2_19

}

TY - CHAP

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

AU - Inoue, Kae

AU - Nakada, Hitoshi

PY - 2018/1/1

Y1 - 2018/1/1

N2 - For given positive integers dj, 1 ⩽ j⩽ ∀ s, ∑j=1sdj even, we construct a piecewise rotation map of the circle with ∑j=1 sdj+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=1 sdj+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.

UR - http://www.scopus.com/inward/record.url?scp=85048679266&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048679266&partnerID=8YFLogxK

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 -