Mather <i>β</i>-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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-for...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/24/11/1600 |
| _version_ | 1827646676135837696 |
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| author | Michael Bialy |
| author_facet | Michael Bialy |
| author_sort | Michael Bialy |
| collection | DOAJ |
| description | The goal of the first part of this note is to get an explicit formula for rotation number and Mather <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-function to rigidity problem. |
| first_indexed | 2024-03-09T19:05:50Z |
| format | Article |
| id | doaj.art-cc82e2012c344a9e865f9ed5fbdefc67 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T19:05:50Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-cc82e2012c344a9e865f9ed5fbdefc672023-11-24T04:36:53ZengMDPI AGEntropy1099-43002022-11-012411160010.3390/e24111600Mather <i>β</i>-Function for Ellipses and RigidityMichael Bialy0School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel Aviv 6997801, IsraelThe goal of the first part of this note is to get an explicit formula for rotation number and Mather <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-function to rigidity problem.https://www.mdpi.com/1099-4300/24/11/1600Birkhoff billiardinvariant curveaction minimizers: rigidity, integrable billiards |
| spellingShingle | Michael Bialy Mather <i>β</i>-Function for Ellipses and Rigidity Entropy Birkhoff billiard invariant curve action minimizers: rigidity, integrable billiards |
| title | Mather <i>β</i>-Function for Ellipses and Rigidity |
| title_full | Mather <i>β</i>-Function for Ellipses and Rigidity |
| title_fullStr | Mather <i>β</i>-Function for Ellipses and Rigidity |
| title_full_unstemmed | Mather <i>β</i>-Function for Ellipses and Rigidity |
| title_short | Mather <i>β</i>-Function for Ellipses and Rigidity |
| title_sort | mather i β i function for ellipses and rigidity |
| topic | Birkhoff billiard invariant curve action minimizers: rigidity, integrable billiards |
| url | https://www.mdpi.com/1099-4300/24/11/1600 |
| work_keys_str_mv | AT michaelbialy matheribifunctionforellipsesandrigidity |