I will give an overview of recent results regarding the behavior
\nof the Poisson bracket under perturbations of the functions relative to
\ndifferent topologies. It turns out that it exhibits both rigidity and
\nflexibility. For instance, if the Poisson bracket of F, G is nonzero, then
\nit cannot be made to vanish by arbitrarily small C^0 perturbations of F, G,
\ndue to a result of Cardin and Viterbo. However if the perturbations are
\nallowed in L^p topology for finite p, then certain flexibility appears, due
\nto recent results by K. Samvelyan. Finally I’ll discuss some fresh results
\nin dimension two, which are part of joint work in progress with K.
\nSamvelyan.<\/p>\n","protected":false},"excerpt":{"rendered":"
I will give an overview of recent results regarding the behavior of the Poisson bracket under perturbations of the functions relative to different topologies. It turns out that it exhibits both rigidity and flexibility. For instance, if the Poisson bracket…
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