# American Institute of Mathematical Sciences

July  2007, 1(3): 465-475. doi: 10.3934/jmd.2007.1.465

## Quasi-states and the Poisson bracket on surfaces

 1 School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel

Received  February 2007 Revised  March 2007 Published  April 2007

We present a convexity-type result concerning simple quasi-states on closed manifolds. As a corollary, an inequality emerges which relates the Poisson bracket to the measure of non-additivity of a simple quasi-state on a closed surface equipped with an area form. In addition, we prove that the uniform norm of the Poisson bracket of two functions on a surface is stable from below under $C^0$-perturbations.
Citation: Frol Zapolsky. Quasi-states and the Poisson bracket on surfaces. Journal of Modern Dynamics, 2007, 1 (3) : 465-475. doi: 10.3934/jmd.2007.1.465
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