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

Quasi-states and the Poisson bracket on surfaces

Frol Zapolsky 1,

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.
Keywords: quasi-states, Poisson bracket, surfaces..
Mathematics Subject Classification: Primary: 53D99 Secondary: 28C1.
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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