English

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