Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Revealing the phase space structure of Hamiltonian systems using the
  action   In this work, we analyse the properties of the Maupertuis' action as a tool
to reveal the phase space structure for Hamiltonian systems. We construct a
scalar field with the action's values along the trajectories in the phase
space. The different behaviour of the trajectories around important phase space
objects like unstable periodic orbits, their stable and unstable manifolds, and
KAM islands generate characteristic patterns on the scalar field constructed
with the action. Using these different patterns is possible to identify the
skeleton of the phase space and understand the dynamics. Also, we present a
simple argument based on the conservation of the energy and the behaviour of
the trajectories to understand the values of their actions. In order to show
how this tool reveals the phase space structures and its effectiveness, we
compare the scalar field constructed with the actions with Poincare maps for
the same set of initial conditions in the phase space of an open Hamiltonian
system with 2 degrees of freedom.

11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph