Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transits close to the Lagrangian solutions $L_1,L_2$ in the Elliptic
  Restricted Three-body Problem   In the last decades a peculiar family of solutions of the Circular Restricted
Three Body Problem has been used to explain the temporary captures of small
bodies and spacecrafts by a planet of the Solar System. These solutions, which
transit close to the Lagrangian points $L_1,L_2$ of the CRTBP, have been
classified using the values of approximate local integrals and of the Jacobi
constant. The use for small bodies of the Solar System requires to consider a
hierarchical extension of the model, from the CRTBP to the the full $N$
planetary problem. The Elliptic Restricted Three Body, which is the first
natural extension of the CRTBP, represents already a challenge, since global
first integrals such as the Jacobi constant are not known for this problem. In
this paper we extend the classification of the transits occurring close to the
Lagrangian points $L_1,L_2$ of the ERTBP using a combination of the Floquet
theory and Birkhoff normalizations. Provided that certain non-resonance
conditions are satisfied, we conjugate the Hamiltonian of the problem to an
integrable normal form Hamiltonian with remainder, which is used to define
approximate local first integrals and to classify the transits of orbits
through a neighbourhood of the Lagrange equilibria according to the values of
these integrals. We provide numerical demonstrations for the Earth-Moon ERTBP.

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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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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: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin