Poisson brackets, quasi-states and symplectic integrators

Michael Entov, Leonid Polterovich, Daniel Rosen

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

This paper is a fusion of a survey and a research article. We focus on certain rigidity phenomena in function spaces associated to a symplectic manifold. Our starting point is a lower bound obtained in an earlier paper with Zapolsky for the uniform norm of the Poisson bracket of a pair of functions in terms of symplectic quasi-states. After a short review of the theory of symplectic quasi-states we extend this bound to the case of iterated Poisson brackets. A new technical ingredient is the use of symplectic integrators. In addition, we discuss some applications to symplectic approximation theory and present a number of open problems.

Original languageEnglish
Pages (from-to)1455-1465
Number of pages11
JournalDiscrete and Continuous Dynamical Systems
Volume28
Issue number4
DOIs
StatePublished - Dec 2010

Keywords

  • Poisson brackets
  • Quasi-states
  • Symplectic approximation theory
  • Symplectic integrators

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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