A Liouville’s Formula for Systems with Reflection
In this work, we derived an Abel–Jacobi–Liouville identity for the case of two-dimensional linear systems of ODEs (ordinary differential equations) with reflection. We also present a conjecture for the general case and an application to coupled harmonic oscillators.
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/8/866 |
| _version_ | 1797412186909310976 |
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| author | Santiago Codesido F. Adrián F. Tojo |
| author_facet | Santiago Codesido F. Adrián F. Tojo |
| author_sort | Santiago Codesido |
| collection | DOAJ |
| description | In this work, we derived an Abel–Jacobi–Liouville identity for the case of two-dimensional linear systems of ODEs (ordinary differential equations) with reflection. We also present a conjecture for the general case and an application to coupled harmonic oscillators. |
| first_indexed | 2024-03-09T04:58:24Z |
| format | Article |
| id | doaj.art-abd3ef3a53cb4098a431875263a7e384 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T04:58:24Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-abd3ef3a53cb4098a431875263a7e3842023-12-03T13:03:19ZengMDPI AGMathematics2227-73902021-04-019886610.3390/math9080866A Liouville’s Formula for Systems with ReflectionSantiago Codesido0F. Adrián F. Tojo1Analytical Sciences Group, Faculty of Sciences, Université de Genève, 1206 Geneva, SwitzerlandInstituto de Matemáticas, Universidade de Santiago de Compostela, 15705 Santiago de Compostela, SpainIn this work, we derived an Abel–Jacobi–Liouville identity for the case of two-dimensional linear systems of ODEs (ordinary differential equations) with reflection. We also present a conjecture for the general case and an application to coupled harmonic oscillators.https://www.mdpi.com/2227-7390/9/8/866ODEs (ordinary differential equations)reflectionlinear systemsLiouville’s formula |
| spellingShingle | Santiago Codesido F. Adrián F. Tojo A Liouville’s Formula for Systems with Reflection Mathematics ODEs (ordinary differential equations) reflection linear systems Liouville’s formula |
| title | A Liouville’s Formula for Systems with Reflection |
| title_full | A Liouville’s Formula for Systems with Reflection |
| title_fullStr | A Liouville’s Formula for Systems with Reflection |
| title_full_unstemmed | A Liouville’s Formula for Systems with Reflection |
| title_short | A Liouville’s Formula for Systems with Reflection |
| title_sort | liouville s formula for systems with reflection |
| topic | ODEs (ordinary differential equations) reflection linear systems Liouville’s formula |
| url | https://www.mdpi.com/2227-7390/9/8/866 |
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