Mather β-Function for Ellipses and Rigidity

The goal of the first part of this note is to get an explicit formula for rotation number and Mather [Formula: see text]-function for ellipse. This is done here with the help of non-standard generating function of billiard problem. In this way the derivation is especially simple. In the second part...

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Detalles Bibliográficos
Autor principal: Bialy, Michael
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9689066/
https://www.ncbi.nlm.nih.gov/pubmed/36359689
http://dx.doi.org/10.3390/e24111600
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author Bialy, Michael
author_facet Bialy, Michael
author_sort Bialy, Michael
collection PubMed
description The goal of the first part of this note is to get an explicit formula for rotation number and Mather [Formula: see text]-function for ellipse. This is done here with the help of non-standard generating function of billiard problem. In this way the derivation is especially simple. In the second part we discuss application of Mather [Formula: see text]-function to rigidity problem.
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spelling pubmed-96890662022-11-25 Mather β-Function for Ellipses and Rigidity Bialy, Michael Entropy (Basel) Article The goal of the first part of this note is to get an explicit formula for rotation number and Mather [Formula: see text]-function for ellipse. This is done here with the help of non-standard generating function of billiard problem. In this way the derivation is especially simple. In the second part we discuss application of Mather [Formula: see text]-function to rigidity problem. MDPI 2022-11-03 /pmc/articles/PMC9689066/ /pubmed/36359689 http://dx.doi.org/10.3390/e24111600 Text en © 2022 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Bialy, Michael
Mather β-Function for Ellipses and Rigidity
title Mather β-Function for Ellipses and Rigidity
title_full Mather β-Function for Ellipses and Rigidity
title_fullStr Mather β-Function for Ellipses and Rigidity
title_full_unstemmed Mather β-Function for Ellipses and Rigidity
title_short Mather β-Function for Ellipses and Rigidity
title_sort mather β-function for ellipses and rigidity
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9689066/
https://www.ncbi.nlm.nih.gov/pubmed/36359689
http://dx.doi.org/10.3390/e24111600
work_keys_str_mv AT bialymichael matherbfunctionforellipsesandrigidity

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