A comparison of symplectic homogenization and Calabi quasi-states

Alexandra Monzner and Frol Zapolsky

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Submission date: 13. Sep. 2010
Pages: 25
published in: Journal of topology and analysis, 3 (2011) 3, p. 243-263 
DOI number (of the published article): 10.1142/S1793525311000581
Bibtex
MSC-Numbers: 53D99, 58C35
Keywords and phrases: symplectic homogenization, quasi-states, Hofer geometry
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Abstract:
We compare two functionals defined on the space of continuous functions with compact support in an open neighborhood of the zero section of the cotangent bundle of a torus. One comes from Viterbo’s symplectic homogenization, the other from the Calabi quasi-states due to Entov and Polterovich. In dimension 2 we are able to say when these two functionals are equal. A partial result in higher dimensions is presented. We also indicate a link to asymptotic Hofer geometry on T*S^1. Proofs are based on the theory of quasi-integrals and topological measures on locally compact spaces.