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arXiv · 2308.13058

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

Eduardo Garibaldi·Samuel Petite·Philippe Thieullen
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Abstract

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.

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Eduardo Garibaldi, Samuel Petite, Philippe Thieullen. 2024-11-08. Classification of discrete weak KAM solutions on linearly repetitive quasi-periodic sets. https://arxiv.org/abs/2308.13058

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