Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sasakian structure associated with a second order ODE and Hamiltonian
  dynamical systems   We define a contact metric structure on the manifold corresponding to a
second order ordinary differential equation $d^2y/dx^2=f(x,y,y')$ and show that
the contact metric structure is Sasakian if and only if the 1-form
$\frac{1}{2}(dp-fdx)$ defines a Poisson structure. We consider a Hamiltonian
dynamical system defined by this Poisson structure and show that the
Hamiltonian vector field, which is a multiple of the Reeb vector field, admits
a compatible bi-Hamiltonian structure for which $f$ can be regarded as a
Hamiltonian function. As a particular case, we give a compatible bi-Hamiltonian
structure of the Reeb vector field such that the structure equations correspond
to the Maurer-Cartan equations of an invariant coframe on the Heisenberg group
and the independent variable plays the role of a Hamiltonian function. We also
show that the first Chern class of the normal bundle of an integral curve of a
multiple of the Reeb vector field vanishes iff $f_x+ff_p = \Psi (x)$ for some
$\Psi$.

13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: eess