Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Queer Poisson brackets   We give a method to construct Poisson brackets $\{\cdot,\cdot\}$ on Banach
manifolds~$M$, for which the value of $\{f,g\}$ at some point $m\in M$ may
depend on higher order derivatives of the smooth functions $f,g\colon
M\to{\mathbb R}$, and not only on the first-order derivatives, as it is the
case on all finite-dimensional manifolds. We discuss specific examples in this
connection, as well as the impact on the earlier research on Poisson geometry
of Banach manifolds. Those brackets are counterexamples to the claim that the
Leibniz property for any Poisson bracket on a Banach manifold would imply the
existence of a Poisson tensor for that bracket.

36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys