Search

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
49/2010

On almost Poisson commutativity in dimension two

Frol Zapolsky

Abstract

Consider the following question: given two functions on a symplectic manifold whose Poisson bracket is small, is it possible to approximate them in the C^0 norm by commuting functions? We give a positive answer in dimension two, as a particular case of a more general statement which applies to functions on a manifold with a volume form. This result is based on a lemma in the spirit of geometric measure theory. We give some immediate applications to function theory and the theory of quasi-states on surfaces with area forms.

Received:
Sep 13, 2010
Published:
Dec 15, 2010
MSC Codes:
53D05, 58C35
Keywords:
Poisson bracket, quasi-states, surfaces

Related publications

inJournal
2010 Journal Open Access
Frol Zapolsky

On almost Poisson commutativity in dimension two

In: Electronic research announcements in mathematical sciences, 17 (2010), pp. 155-160