Classification of discrete weak KAM solutions on linearly repetitive quasi-periodic sets
Mathematical Physics
2024-11-11 v2 Classical Analysis and ODEs
Dynamical Systems
math.MP
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.
Keywords
Cite
@article{arxiv.2308.13058,
title = {Classification of discrete weak KAM solutions on linearly repetitive quasi-periodic sets},
author = {Eduardo Garibaldi and Samuel Petite and Philippe Thieullen},
journal= {arXiv preprint arXiv:2308.13058},
year = {2024}
}
Comments
53 pages, 7 figures