Strict sub-solutions and Mañe potential in discrete weak KAM theory

Details Strict sub-solutions and Mañe potential in discrete weak KAM theory Strict sub-solutions and Mañe potential in discrete weak KAM theory

2009-05-05

arxiv.org/abs/0905.0615v1

Mathematics

Dynamical Systems

49 pages

Scientific paper

In this paper, we explain some facts on the discrete case of weak KAM theory. In that setting, the Lagrangian is replaced by a cost $c:X\times X \to \mathbb{R}$, on a "reasonable" space $X$. This covers for example the case of periodic time-dependent Lagrangians. As is well known, it is possible in that case to adapt most of weak KAM theory. A major difference is that critical sub-solutions are not necessarily continuous. We will show how to define a Ma\~ne potential. In contrast to the Lagrangian case, this potential is not continuous. We will recover the Aubry set from the set of continuity points of the Ma\~ne potential, and also from critical sub-solutions.

Affiliated with

Also associated with

No associations

Rating

Strict sub-solutions and Mañe potential in discrete weak KAM theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Strict sub-solutions and Mañe potential in discrete weak KAM theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Strict sub-solutions and Mañe potential in discrete weak KAM theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-450756