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

Kae Inoue, Hitoshi Nakada

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

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.

Original languageEnglish
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Pages393-431
Number of pages39
DOIs
Publication statusPublished - 2018 Jan 1

Publication series

NameLecture Notes in Mathematics
Volume2213
ISSN (Print)0075-8434

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ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Inoue, K., & Nakada, H. (2018). A Piecewise rotation of the circle, IPR maps and their connection with translation surfaces. In 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