Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lie-Poisson methods for isospectral flows   The theory of isospectral flows comprises a large class of continuous
dynamical systems, particularly integrable systems and Lie--Poisson systems.
Their discretization is a classical problem in numerical analysis. Preserving
the spectra in the discrete flow requires the conservation of high order
polynomials, which is hard to come by. Existing methods achieving this are
complicated and usually fail to preserve the underlying Lie--Poisson structure.
Here we present a class of numerical methods of arbitrary order for Hamiltonian
and non-Hamiltonian isospectral flows, which preserve both the spectra and the
Lie--Poisson structure. The methods are surprisingly simple, and avoid the use
of constraints or exponential maps. Furthermore, due to preservation of the
Lie--Poisson structure, they exhibit near conservation of the Hamiltonian
function. As an illustration, we apply the methods to several classical
isospectral flows.

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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas