The three gap theorem asserts that for any real \\α\ and any positive integer \N\ the fractional parts of the sequence \0, \α, 2\α, \⋯, (N-1)\α\ have at most three distinct gap lengths. In this note, we extend the three gap theorem to arbitrary orbits of interval exchange transformations, and in the process, we generalize the three gap theorem and a result by Boshernitzan.
SEEK ID: https://publications.h-its.org/publications/1465
DOI: 10.1093/imrn/rnab319
Research Groups: Groups and Geometry
Publication type: Journal
Journal: International Mathematics Research Notices
Citation: International Mathematics Research Notices,rnab319
Date Published: 24th Nov 2021
URL: https://doi.org/10.1093/imrn/rnab319
Registered Mode: imported from a bibtex file
Views: 3977
Created: 21st Feb 2022 at 14:33
Last updated: 5th Mar 2024 at 21:24
This item has not yet been tagged.
None