XXXVII Workshop on Geometric Methods in Physics 1-7.07.2018
VII School on Geometry and Physics 25-29.06.2018

Tomasz Goliński

Queer Poisson brackets on Banach manifolds

It turns out that Poisson brackets on Banach manifolds $M$ defined as a bilinear map from $C^\infty(M)\times C^\infty(M)$ to $C^\infty(M)$ satisfying Leibniz and Jacobi conditions may not be given by Poisson tensors. Their value at some point may depend on higher order derivatives of functions. We present a specific example of such Poisson bracket on $l^p$ spaces. From physical point of view these brackets are pathological, as the Hamiltonian vector fields don't lead to flows on $M$.

The talk is based on joint work with D. Beltita and A.B. Tumpach:

Event sponsored by:
of Bialystok
University of Bialystok

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