Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Factorization dynamics and Coxeter-Toda lattices   It is shown that the factorization relation on simple Lie groups with
standard Poisson Lie structure restricted to Coxeter symplectic leaves gives an
integrable dynamical system. This system can be regarded as a discretization of
the Toda flow. In case of $SL_n$ the integrals of the factorization dynamics
are integrals of the relativistic Toda system. A substantial part of the paper
is devoted to the study of symplectic leaves in simple complex Lie groups, its
Borel subgroups and their doubles.

29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
3
The categories of this paper are: physics
18
The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con