Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A class of integrable Hamiltonian systems including scattering of
  particles on the line with repulsive interactions   The main purpose of this paper is to introduce a new class of Hamiltonian
scattering systems of the cone potential type that can be integrated via the
asymptotic velocity. For a large subclass, the asymptotic data of the
trajectories define a global canonical diffeomorphism $A$ that brings the
system into the normal form $\dot P=0$, $\dot Q=P$.
  The integrability theory applies for example to a system of $n$ particles on
the line interacting pairwise through rather general repulsive potentials. The
inverse $r$-power potential for arbitrary $r>0$ is included, the reduction to
normal form being carried out for the exponents $r>1$. In particular, the
Calogero system is obtained for $r=2$. The treatment covers also the
nonperiodic Toda lattice.
  The cone potentials that we allow can undergo small perturbations in any
arbitrary compact set without losing the integrability and the reduction to
normal form.

4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
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The categories of this paper are: q-alg