Aubry-Mather theory and idempotent eigenfunctions of the Bellman operator

Details Aubry-Mather theory and idempotent eigenfunctions of the Bellman operator Aubry-Mather theory and idempotent eigenfunctions of the Bellman operator

1999-06-23

arxiv.org/abs/chao-dyn/9906036v2

Comm. Contemporary Math. 1:4 (1999) 517-533

Mathematics

Dynamical Systems

16 pages, no figures; some typos corrected and the reference included

Scientific paper

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.

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