English

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