Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symplectic integration of boundary value problems   Symplectic integrators can be excellent for Hamiltonian initial value
problems. Reasons for this include their preservation of invariant sets like
tori, good energy behaviour, nonexistence of attractors, and good behaviour of
statistical properties. These all refer to {\em long-time} behaviour. They are
directly connected to the dynamical behaviour of symplectic maps $\varphi\colon
M\to M$ on the phase space under iteration. Boundary value problems, in
contrast, are posed for fixed (and often quite short) times. Symplecticity
manifests as a symplectic map $\varphi\colon M\to M'$ which is not iterated. Is
there any point, therefore, for a symplectic integrator to be used on a
Hamiltonian boundary value problem? In this paper we announce results that
symplectic integrators preserve bifurcations of Hamiltonian boundary value
problems and that nonsymplectic integrators do not.

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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio