Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction
We consider the limit N→+∞ of N-body type problems with weak interaction, equal masses and −σ-homogeneous potential, 0<σ<1. We obtain the integro-differential equation that the motions must satisfy, with limit choreographic solutions corresponding to travelling waves of this equation. Such equ...
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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2016 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148005 |
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| Цитувати: | Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction / R. Castaneira, P. Padilla, H. Sánchez-Morgado // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 8 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-148005 |
|---|---|
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dspace |
| spelling |
irk-123456789-1480052019-02-17T01:25:23Z Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction Castaneira, R. Padilla, P. Sánchez-Morgado, H. We consider the limit N→+∞ of N-body type problems with weak interaction, equal masses and −σ-homogeneous potential, 0<σ<1. We obtain the integro-differential equation that the motions must satisfy, with limit choreographic solutions corresponding to travelling waves of this equation. Such equation is the Euler-Lagrange equation of a corresponding limiting action functional. Our main result is that the circle is the absolute minimizer of the action functional among zero mean (travelling wave) loops of class H¹. 2016 Article Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction / R. Castaneira, P. Padilla, H. Sánchez-Morgado // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 8 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 70F45; 70G75; 70F10 DOI:10.3842/SIGMA.2016.104 http://dspace.nbuv.gov.ua/handle/123456789/148005 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We consider the limit N→+∞ of N-body type problems with weak interaction, equal masses and −σ-homogeneous potential, 0<σ<1. We obtain the integro-differential equation that the motions must satisfy, with limit choreographic solutions corresponding to travelling waves of this equation. Such equation is the Euler-Lagrange equation of a corresponding limiting action functional. Our main result is that the circle is the absolute minimizer of the action functional among zero mean (travelling wave) loops of class H¹. |
| format |
Article |
| author |
Castaneira, R. Padilla, P. Sánchez-Morgado, H. |
| spellingShingle |
Castaneira, R. Padilla, P. Sánchez-Morgado, H. Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Castaneira, R. Padilla, P. Sánchez-Morgado, H. |
| author_sort |
Castaneira, R. |
| title |
Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction |
| title_short |
Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction |
| title_full |
Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction |
| title_fullStr |
Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction |
| title_full_unstemmed |
Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction |
| title_sort |
continuous choreographies as limiting solutions of n-body type problems with weak interaction |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148005 |
| citation_txt |
Continuous Choreographies as Limiting Solutions of N-body Type Problems with Weak Interaction / R. Castaneira, P. Padilla, H. Sánchez-Morgado // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 8 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT castaneirar continuouschoreographiesaslimitingsolutionsofnbodytypeproblemswithweakinteraction AT padillap continuouschoreographiesaslimitingsolutionsofnbodytypeproblemswithweakinteraction AT sanchezmorgadoh continuouschoreographiesaslimitingsolutionsofnbodytypeproblemswithweakinteraction |
| first_indexed |
2023-05-20T17:29:01Z |
| last_indexed |
2023-05-20T17:29:01Z |
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1796153397402927104 |