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MiS Preprint

On almost Poisson commutativity in dimension two

Frol Zapolsky


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.

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

Related publications

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