Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On $k$-jet field approximations to geodesic deviation equations   Let $M$ be a smooth manifold and $\mathcal{S}$ a semi-spray defined on a
sub-bundle $\mathcal{C}$ of the tangent bundle $TM$. In this work it is proved
that the only non-trivial $k$-jet approximation to the exact geodesic deviation
equation of $\mathcal{S}$, linear on the deviation functions and invariant
under an specific class of local coordinate transformations is the Jacobi
equation. However, if the linearity property on the dependence in the deviation
functions is not imposed, then there are differential equations whose solutions
admit $k$-jet approximations and are invariant under arbitrary coordinate
transformations. As an example of higher order geodesic deviation equations we
study the first and second order geodesic deviation equations for a Finsler
spray.

29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th