Mathematics – Dynamical Systems
Scientific paper
2010-01-18
Mathematics
Dynamical Systems
Scientific paper
In 1996, Ricardo Ricardo Ma\~n\'e discovered that Mather measures are in fact the minimizers of a "universal" infinite dimensional linear programming problem. This fundamental result has many applications, one of the most important is to the estimates of the generic number of Mather measures. Ma\~n\'e obtained the first estimation of that sort by using finite dimensional approximations. Recently, we were able with Gonzalo Contreras to use this method of finite dimensional approximation in order to solve a conjecture of John Mather concerning the generic number of Mather measures for families of Lagrangian systems. In the present paper we obtain finer results in that direction by applying directly some classical tools of convex analysis to the infinite dimensional problem. We use a notion of countably rectifiable sets of finite codimension in Banach (and Frechet) spaces which may deserve independent interest.
No associations
LandOfFree
On the number of Mather measures of Lagrangian systems 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 On the number of Mather measures of Lagrangian systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the number of Mather measures of Lagrangian systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-661388