A Liouville’s Formula for Systems with Reflection

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.

Bibliographic Details
Main Authors: Santiago Codesido, F. Adrián F. Tojo
Format: Article
Language:English
Published: MDPI AG 2021-04-01
Series:Mathematics
Subjects:
ODEs (ordinary differential equations)
reflection
linear systems
Liouville’s formula
Online Access:https://www.mdpi.com/2227-7390/9/8/866
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spelling doaj-abd3ef3a53cb4098a431875263a7e3842021-04-15T23:00:43ZengMDPI AGMathematics2227-73902021-04-01986686610.3390/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
collection DOAJ
language English
format Article
sources DOAJ
author Santiago Codesido
F. Adrián F. Tojo
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
author_facet Santiago Codesido
F. Adrián F. Tojo
author_sort Santiago Codesido
title A Liouville’s Formula for Systems with Reflection
title_short 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_sort liouville’s formula for systems with reflection
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-04-01
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.
topic ODEs (ordinary differential equations)
reflection
linear systems
Liouville’s formula
url https://www.mdpi.com/2227-7390/9/8/866
work_keys_str_mv AT santiagocodesido aliouvillesformulaforsystemswithreflection
AT fadrianftojo aliouvillesformulaforsystemswithreflection
AT santiagocodesido liouvillesformulaforsystemswithreflection
AT fadrianftojo liouvillesformulaforsystemswithreflection
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