Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Low-dimensional chaos in the single wave model for self-consistent
  wave-particle Hamiltonian   We analyze nonlinear aspects of the self-consistent wave-particle interaction
using Hamiltonian dynamics in the single wave model, where the wave is modified
due to the particle dynamics. This interaction plays an important role in the
emergence of plasma instabilities and turbulence. The simplest case, where one
particle (N = 1) is coupled with one wave (M = 1), is completely integrable,
and the nonlinear effects reduce to the wave potential pulsating while the
particle either remains trapped or circulates forever. On increasing the number
of particles (N = 2, M = 1), integrability is lost and chaos develops. Our
analyses identify the two standard ways for chaos to appear and grow (the
homoclinic tangle born from a separatrix, and the resonance overlap near an
elliptic fixed point). Moreover, a strong form of chaos occurs when the energy
is high enough for the wave amplitude to vanish occasionally.

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The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
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The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph