Aubry-Mather theory and idempotent eigenfunctions of the Bellman operator
chao-dyn
2016-08-31 v2 Dynamical Systems
Chaotic Dynamics
Abstract
We establish a connection between the Aubry-Mather theory of invariant sets of a 1D dynamical system described by a Lagrangian with potential periodic in space and time, on the one hand, and idempotent spectral theory of the Bellman operator of the corresponding optimization problem, on the other hand. This connection is applied to obtain a uniqueness result for an eigenfunction of the Bellman operator in the case of irrational rotation number.
Keywords
Cite
@article{arxiv.chao-dyn/9906036,
title = {Aubry-Mather theory and idempotent eigenfunctions of the Bellman operator},
author = {Andrei Sobolevskii},
journal= {arXiv preprint arXiv:chao-dyn/9906036},
year = {2016}
}
Comments
16 pages, no figures; some typos corrected and the reference included