Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On homoclinic orbits to center manifolds of elliptic-hyperbolic
  equilibria in Hamiltonian systems   We consider a Hamiltonian system which has an elliptic-hyperbolic equilibrium
with a homoclinic loop. We identify the set of orbits which are homoclinic to
the center manifold of the equilibrium via a Lyapunov- Schmidt reduction
procedure. This leads to the study of a singularity which inherits certain
structure from the Hamiltonian nature of the system. Under non-degeneracy
assumptions, we classify the possible Morse indices of this singularity,
permitting a local description of the set of homoclinic orbits. We also
consider the case of time-reversible Hamiltonian systems.

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The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: stat