Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

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