Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: H\"older stability for $C^r$ central translations   We consider the class of diffeomorphisms of a manifold that its differential
keeps invariant a one-dimensional subbundle $E$. For that type of
diffeomorphisms is naturally defined a one-parameter family called
$E-$translation. We prove that if a diffeomorphisms in above mentioned class is
conjugate to its $E-$translation and the conjugacy is at distance
$\alpha$-H\"older to the identity respect to the parameter and $\alpha>1/2$,
then the $E$-direction is hyperbolic.
  This theorem is also sharp as it is be discussed with some examples. We also
deal with the continuously stable case in the Skew-Products context with
one-dimensional fibers, requiring extra hypothesis along the fibers like either
non-negative second derivative or negative Schwartzian.

37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex