Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tri-hamiltonian Toda lattice and a canonical bracket for closed discrete
  curves   Flows on (or variations of) discrete curves in $\R^2$ give rise to flows on a
subalgebra of functions on that curve. For a special choice of flows and a
certain subalgebra this is described by the Toda lattice hierachy. In the paper
it is shown that the canonical symplectic structure on $\R^{2N}$, which can be
interpreted as the phase space of closed discrete curves in $\R^2$ with length
$N,$ induces Poisson commutation relations on the above mentioned subalgebra
which yield the tri-hamiltonian poisson structure of the Toda lattice hierachy.

31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph