Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coherent Riemannian-geometric description of Hamiltonian order and chaos
  with Jacobi metric   By identifying Hamiltonian flows with geodesic flows of suitably chosen
Riemannian manifolds, it is possible to explain the origin of chaos in
classical Newtonian dynamics and to quantify its strength. There are several
possibilities to geometrize Newtonian dynamics under the action of conservative
potentials and the hitherto investigated ones provide consistent results.
However, it has been recently argued that endowing configuration space with the
Jacobi metric is inappropriate to consistently describe the
stability/instability properties of Newtonian dynamics because of the
non-affine parametrization of the arc length with physical time. To the
contrary, in the present paper, it is shown that there is no such inconsistency
and that the observed instabilities in the case of integrable systems using the
Jacobi metric are artefacts.

8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
2
The categories of this paper are: math