Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nilpotent integrability, reduction of dynamical systems and a
  third-order Calogero-Moser system   We present an algebraic formulation of the notion of integrability of
dynamical systems, based on a nilpotency property of its flow: it can be
explicitly described as a polynomial on its evolution parameter. Such a
property is established in a purely geometric--algebraic language, in terms
both of the algebra of all higher-order constants of the motion (named the
nilpotent algebra of the dynamics), and of a maximal Abelian algebra of
symmetries (called a Cartan subalgebra of the dynamics). It is shown that this
notion of integrability amounts to the annihilator of the nilpotent algebra
being contained in a Cartan subalgebra of the dynamics. Systems exhibiting this
property will be said to be nilpotent integrable.
  Our notion of nilpotent integrability offers a new insight into the intrinsic
dynamical properties of a system, which is independent of any auxiliary
geometric structure defined on its phase space. At the same time, it extends in
a natural way the classical concept of complete integrability for Hamiltonian
systems. An algebraic reduction procedure valid for nilpotent integrable
systems, generalizing the well-known reduction procedures for symplectic and/or
Poisson systems on appropriate quotient spaces, is also discussed. In
particular, it is shown that a large class of nilpotent integrable systems can
be obtained by reduction of higher-order free systems. The case of the
third-order free system is analyzed and a nontrivial set of third-order
Calogero-Moser-like nilpotent integrable equations is obtained.

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The categories of this paper are: econ
29
The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
3
The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: eess