An Extension of the Three Gap Theorem to Interval Exchange Transformations

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Abstract:

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

Author: Diaaeldin Taha

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Brice Loustau

Citation

Taha, D. (2021). An Extension of the Three Gap Theorem to Interval Exchange Transformations. In International Mathematics Research Notices (Vol. 2023, Issue 4, pp. 2996–3003). Oxford University Press (OUP). https://doi.org/10.1093/imrn/rnab319

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Created: 21st Feb 2022 at 14:33

Last updated: 5th Mar 2024 at 21:24

An Extension of the Three Gap Theorem to Interval Exchange Transformations

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