Classification of discrete weak KAM solutions on linearly repetitive quasi-periodic sets
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913573850054656 |
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| author | Garibaldi, Eduardo Petite, Samuel Thieullen, Philippe |
| author_facet | Garibaldi, Eduardo Petite, Samuel Thieullen, Philippe |
| contents | In discrete schemes, weak KAM solutions may be interpreted as approximations of correctors for some Hamilton-Jacobi equations in the periodic setting. It is known that correctors may not exist in the almost periodic setting. We show the existence of discrete weak KAM solutions for non-degenerate and weakly twist interactions in general. Furthermore, assuming equivariance with respect to a linearly repetitive quasi-periodic set, we completely classify all possible types of weak KAM solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_13058 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Classification of discrete weak KAM solutions on linearly repetitive quasi-periodic sets Garibaldi, Eduardo Petite, Samuel Thieullen, Philippe Mathematical Physics Classical Analysis and ODEs Dynamical Systems 82D25, 82M30, 37J51, 52C23 In discrete schemes, weak KAM solutions may be interpreted as approximations of correctors for some Hamilton-Jacobi equations in the periodic setting. It is known that correctors may not exist in the almost periodic setting. We show the existence of discrete weak KAM solutions for non-degenerate and weakly twist interactions in general. Furthermore, assuming equivariance with respect to a linearly repetitive quasi-periodic set, we completely classify all possible types of weak KAM solutions. |
| title | Classification of discrete weak KAM solutions on linearly repetitive quasi-periodic sets |
| topic | Mathematical Physics Classical Analysis and ODEs Dynamical Systems 82D25, 82M30, 37J51, 52C23 |
| url | https://arxiv.org/abs/2308.13058 |