Classification of discrete weak KAM solutions on linearly repetitive quasi-periodic sets

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...

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Bibliographic Details
Published in:arXiv.org 2024-11
Main Authors: Garibaldi, Eduardo, Petite, Samuel, Thieullen, Philippe
Format: Article
Language:English
Subjects:
Hamilton-Jacobi equation
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Summary: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.
ISSN:2331-8422