Deduciendo el teorema de las tres brechas vía inducción Rauzy-Veech

Autor: Christian Weiss

Publikováno v: Revista Colombiana de Matemáticas, Volume: 54, Issue: 1, Pages: 31-37, Published: JUN 2020

The Three Gap Theorem states that there are at most three distinct lengths of gaps if one places $n$ points on a circle, at angles of $z, 2z, 3z, \ldots nz$ from the starting point. The theorem was first proven in 1958 by S\'os and many proofs have b

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ee670d52debdfff7c7f6adf7a7bb7c60
https://doi.org/10.15446/recolma.v54n1.89777

Renormalization for piecewise smooth homeomorphisms on the circle

Autor: Kleyber Cunha, Daniel Smania

Publikováno v: Repositório Institucional da UFBA
Universidade Federal da Bahia (UFBA)
instacron:UFBA
Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP

In this work we study the renormalization operator acting on piecewise smooth homeomorphisms on the circle, that turns out to be essentially the study of Rauzy-Veech renormalizations of generalized interval exchanges maps with genus one. In particula

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::335d8c1a399187a60039dfbb854b12cc
https://doi.org/10.1016/j.anihpc.2012.09.004

The Khinchin Theorem for interval-exchange transformations

Autor: Luca Marchese

Publikováno v: Journal of Modern Dynamics. 5:123-183

We define a Diophantine condition for interval-exchange transformations. When the number of intervals is two, that is, for rotations on the circle, our condition coincides with the classical Khinchin condition. We prove for interval-exchange transfor

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::082bc14d74440f5b9cb5327aafefa9cc
https://doi.org/10.3934/jmd.2011.5.123

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